So it's a real pleasure to have Professor Martin Mourigal from the School of Physics here at Georgia Tech. Martin got his bachelor's degree in materials at the AQL demeaned of Nancy in France, I hope I pronounced that right. And then his Masters and PhD's, PhD degrees in physics at the Ecole Polytechnique Federale, the EPFL in Switzerland. He then did a post-doctoral stint at Johns Hopkins before coming to Georgia Tech in 2015, where he's currently an associate professor of physics. He's had won a number of awards, most notably 2018 NSF Career Award, and a 2019 Kavli Fellow from the National Academy of Sciences. And with that, I will turn it over to learn. Alright, thank you David. Thanks to IL5 and me. It's a great pleasure to be here and to give a talk in person to all of you. So this is going to be an introduction to some of the ideas we, we explore in my lab and other labs at Georgia Tech with whom we collaborate. And so my interest is in magnetism. And we prefix it with the word quantum magnetism to, to express the ID that low temperature in this magnet, there is genuinely quantum phenomena that we can observe and try to understand. So I came in 2015 versus the group integrated over the years here. And so we were fortunate to have support from the NSF and the Department of Energy, as well as IN Georgia Tech College of Science. And as you will see, we are using national scale facilities to probe this magnets. So that includes neutron sources at Oak Ridge National Lab at that nist in, in, in Gettysburg, Maryland, and also recently started to use a crystal grows facility that is funded by the NSF. And this is the Cornell Johns Hopkins facility. So the outline of the talk is as follows. I want to talk a little bit, but comments matter and how physicists see materials, which is may not be the same way as material. Scientists see materials and we see this in terms of symmetry and phases. And then I will talk about the concept of spin liquids. Where they spin liquids, what they are and how they emerge. And we'll material then how we characterize and studied them, which involves this technique of neutron scattering. And at the end, I will talk a little bit about the current trends in the fields and the sort of things we are trying to, to, to, to get at in research. So the way physicists think about materials is really to classify them according to the asymmetries. And the most simple thing you can imagine, as you have, you're going to have a solid in a liquid. And these two phases of matter are separated by a phase transition at a given temperature. And in some sense you can say liquid does not break an asymmetry, a solid breaks certain symmetries that are translational or rotational. And we can classify essentially all, all solids using crystallography. And there's certain number of space groups that we can use, and so on and so forth. And liquids. Although they don't have broken symmetries, they are still interested, interesting on the, on their own. And in fact, when you are very close to a transition, illiquid is a highly correlated state of matter, so the positions of the atoms are not random and they are correlated. And we will see that this is kind of the same ID in what I will call the spin liquid. Okay? And the traditional way that people have been studying liquids and solids is using, for instance, diffraction, where you can shine a beam here of x-rays on a crystal or a powder, and you collect intensity in the detector, the CEO at an angle two theta and Bragg's Law is giving you okay, well, for a given scattering angle, I can see a different momentum transfer. And I can reconstruct from the momentum transfer the spacing between the atoms in that so we know the structure of materials in the bulk. Okay? And do you have many different ways to do this? So one example here, very simple is just solid neon. And you see here a Bragg diffraction of solid neon. This is an old PLL paper, the 50s. And you see sharp Bragg peaks that are characteristic of, of the solid. Okay? But of course you could warm up. That's, that's the stem here. It's argon. Neon are almost essentially the same. So imagine we just warm up this and we go in the liquid phase and we see that the diffraction, a spectrum of this, or the diffraction pattern of this liquid keeps some of the characteristics of the solid. In particular, they are peaks, but this peaks are broad and diffuse. So liquids keep some organization that informs on the way they're going to crystallize. And this oscillations here and the structure factor or a signature of the correlations between the atoms. So in my research, we essentially do the same, except we use magnetic materials that are liquid in the sense that their spins are not ordered. And instead of using X-rays, we use neutrons to characterize such correlations in matter. Okay? Of course you can also do this on, on crystals and these are some nice 1912 measurements. And this is nowadays measurement on some crystals. So there's been a lot of progress in X-ray diffraction. But one thing that you may not be aware of is that there are certain materials that do not fall into this classification of solids and liquids. One example that physicists like to talk about is liquid ileum. So when you cool liquid helium to low temperatures, it actually does not freeze. And at some temperature of the order of two Kelvin here, you have a phase transition between two phases of the liquid. And this phase transition characterizes the emergence of a macroscopic quantum phenomena that we call super fluidity. So when the system does not freeze, it tends at low temperature to stabilize some quantum state that has special properties, in that case, superfluid. Okay? So that's one example of we would say quantum material. So a quantum liquid, because at low temperature, in absence of freezing, the system behaves according to the laws of quantum mechanics. There are other materials that are interesting to physicists and materials scientists such as liquid crystals. And they are hybrid between solids and liquids in the sense that they break only certain symmetries. And a lot of phenomena can emerge from liquid crystals as well. But here, you know, what I want to talk about today is this idea of spin liquid. And if you type spin liquid in Google, you're going to get this nice illustration from a colleague in the UK. And the first thing you may want to think about is that it's been liquids or liquid like phases of magnetic matter. Okay? But this picture is wrong, okay? This is not, what is spin liquid is, this is not a liquid or spins in that sense. And what's missing from this picture is that this been liquids. The reason we are interested in them is that they are dominated at the atomic scale by quantum entanglement, which of course this picture does not capture. And in the same way that superfluid ileum at low temperature is dominated by a macroscopic quantum phenomena that is super fluidity. Okay? So that's the picture. Let's try to look at this spin liquids. Okay, so where to find them? What are they? That's the first thing I want to try to explain a little bit. Okay? And we will navigate between the concept of what is called a Mott insulator to deriving what is called the Heisenberg model, which is essentially the same, that describes all spin liquids and quantum magnets in general. Okay? So you may have heard about the word quantum matter, and this is what the catchphrase that physicists use to describe a material that is interesting to them. And there are many such quantum materials that do many, many different things. So for instance, the quantum Hall effect, you have a 2D electron gas in high magnetic field. This is a quantum, this is an example of quantum matter. You can imagine topological insulators, topological materials in conventional superconductors of disordered metals, all of these phases are dominated by quantum effects. But one thing that is special about them is that they all have conduction or itinerant electrons. Okay? In my research on Spin liquids, we work with insulators. So the materials do not conduct electricity. And in fact, this is because they do not conduct electricity that a special spin phenomena emerge in the material. And that's what I want to explain a little bit. So we will not talk about materials dominated by electronic conduction. In this talk, we will talk about insulators. And by the way, this is one of the challenge with spin liquids to use them in applications is that they are not, they are not conducting. So how do we functionalize them or do we integrate them in device? So that's something we don't actually know what to do at this point. So let me, let me explain and highlight the way physicists sinks think about materials, which is in some sense from a crystal structure that you may have detail mind with x-ray diffraction to a model that does weird stuff. Okay, So let's talk about this. And as an example, I'm taking a very famous material which is lanthanum copper oxide. It's the perovskite material where you have octahedral of copper surrounded by oxygen and some stacking of this octahedral in, in the system. And the first thing you may want to think about is this material is magnetic. And you might ask, where's the magnetism coming from? Well, the magnetism is coming from local physics of the copper two plus ion. So you have nine electrons to put into the d orbital. And this d orbitals are not degenerate because they are surrounded by oxygen charges. So there's something we call a crystal field. And when you populate all these orbitals with electrons, you end up with one orbital with one electron. And all these orbitals here are filled. So what the physicists do, the truncate this Hilbert space. They discard the physics coming from this filled orbital. And they consider cockpit 2 plus a simple one, spin half in one orbital. So that's already a dramatic reduction of the complexity of the system from a full crystal structure to one electron in one orbital. Okay? If you remember your atomic physics or your chemistry, you remember that this particular orbital is a, is a square planar orbital. And so it means that the spin half moment that lives here in the 3D shell actually leaves kind of in the plane. And so what really matters in lanthanum, copper oxide is just the plane of copper, oxygen. This is where the magnetic physics is taking place. Okay? And we have a way to describe the physicists have a way to describe the physics using the so-called Hubbard model. So you probably heard about this before, but let's, let's just revisit or discuss what the Hubbard model is telling us. Okay? So what the Hubbard model starts from is to say, well, you know, at every site on this crystal we have one electron in one orbital. So I'm going to draw the system like this. And then I'm going to remove the crystal. I'm just going to talk about my orbitals with one electron. That's the next step in the modelling of the system. And then you might just count the electrons and say, Well this is great. I can probably take one electron and there is one electron, one hole per site. So I can probably propagate my electron in the system. And this system should definitely be a metal. There is the possibility for the electrons to move around because there are some empty spots for which they can go. And the first thing you might do is you take two electrons with the same spin and you put them into some orbital and you have a big red flag from quantum mechanics, that is Pauli exclusion principle cannot happen. So then you might say, okay, well I'm going to do something more interesting. I'm going to take expense of different directions on sites that are next to each other. And I can take one electron, I can make it hop here, here, here, here. And you can propagate that electron through the lattice and you pay some kinetic energy. We call it T. The font is a little bit weird. Here is a t. So the kinetic, you gain some kinetic energy by moving the electron like this. So if you believe band structure, this material should be good metal and you can make it in the lab and you're going to get something that looks like a ceramic. Okay? So definitely not a metal, not shiny. So it's already apparent when you synthesized the system. Okay? So why is it not a metal? And the reason is not a metal is that when we do this picture, we forget that electrons interact with each other. And it turns out when you put two electrons on the same site with opposite spins, you have to pay a huge cost in energy, which comes from the electrostatics of the electron-electron interaction. We call this the Coulomb view. This is the interior electron energy. Okay? And so what happens in this type of system is that the Coulomb repulsion is much greater than the kinetic energy. And as a result, although the electrons attempt to hop from one side to the another effectively, they cannot do that because the cost in energy is too high. So this what we call virtual processes. So the electron sample, they are neighboring sites, but they are not able to propagate as a conduction electron. Okay? So, so as a result of this, there is a localization of the electrons on the lattice sites. But because of Pauli exclusion principle, you see that two neighboring sites of opposite spin. Okay? So that's the emergence of what we call an antiferromagnetic insulator out of a system with one electron per unit cell that should otherwise be a conductor. Okay? And so then I can bring back my crystal, I repopulate with my crystal and I put some spins and I have an anti ferromagnet. Okay? So lanthanum copper oxide, because of strong correlations between electrons, is an antiferromagnetic insulator. Okay, So now what do we have to do to understand this material? Well, we are left with one spin per site, and now we can start to understand how the spins interact with each other and how they excitations may behave in the system. And it turns out that the spin excitations are the lowest energy excitation in the system. This is what happens at low temperature and in this system, okay? And in particular there is long-range magnetic order. So out of all of this complicated technology or theoretical technology, emerges a very simple model that was actually invented before we knew about the Hubbard model, which is called the Heisenberg model. And the Heisenberg model is a simple model that says that if you have two spins that are nearest neighbor on the lattice, there is a certain cost in energy associated with their dot-product. We call this the exchange interaction. It turns out the exchange interaction can be derived as a function of the parameters t and u is t square over you. And for reasons I don't have time to explain, but that involved the ligands that participate also in this, in this phenomena, this exchange interaction can be negative. And if you minimize the energy, you're going to get two spins align or it can be positive. You have antiferromagnetic interaction. So the Eisenberg model is a very simple model of mechanism that can be derived from first principles, if you wish, from a larger electronic system that is here, lanthanum as an example, lanthanum copper oxide. So this model was formulated in 1935, I believe, and we are still working on it every day in my lab in many other, he lives in the world. People are trying to understand the Heisenberg model, okay? In all its different variations. Okay? So if you have a good model, then you can study it until you retire. Okay? Do not ever solve it, okay? If you have a good model, do not solve it, continue to, to try to understand it. Okay, good. So that's what we're going to focus on and I'm going to, to, to explain a bit this idea of quantum mechanism are going to work with a very simple system. Now, I'm going to remove lanthanum copper oxide from your head. Imagine you have two spins and they are coupled with exchange interactions. And I want to know the ground-state of that stuff. What can be the ground state? Well, you can go to an undergrad quantum mechanics textbook and you will learn that you need to describe this using so-called Hilbert space. And the dimension of that Hilbert space will grow as two to the n, where n is the number of Spence. And here we have two spins that we have a four by four matrix to diagonalize. And this is Georgia Tech. We can do that, okay? Although sometimes we get surprises. When we assign such exams in quantum mechanics one. But anyway, so you can diagonalize this problem. And what you find is that although classically, classically you would say if I have an antiferromagnetic, well I'm going to put one spin up and one spin down. That's my ground state. But it turns out that quantum mechanically with this breaks rotation symmetry. So this is not a good ground state and a good ground state is actually a quantum superposition of spin up and down and up, down and up. And you have a singlet state which corresponds to the quantum superposition of these two up, down and Don upstate. So that's what the ground state of a dimer of two spins is. And then you have an excited state that is separated by a gap of the order of the exchange interaction. And that excited state is the triplet state. So you have two spins up to spins down and the contour in the symmetric superposition of these two things. Okay, so that's undergraduate quantum mechanics to spins interacting antiferromagnetic lead. The ground state is not magnetic because it's a quantum superposition of up, down and up. Okay? So now of course, we can actually prepare materials that have this kind of dimers structures. And these have been studies in the nineties quite a lot. But it's more interesting to consider know an extended system like you would get in a real crystal. For instance, a chain of spin-offs interacting antiferromagnetic. And it turns out this problem can be solved exactly or can be solved approximately with very advanced numerical techniques. We have some specialist at Georgia Tech in particular doing tensor network techniques. But we know the ground state exactly. But it's not useful for presentation at that level. So what I will do is just use my knowledge of the two spins problem and say, well, you know what? I'm going to just take my chain and I'm going to divide it in even, in odd pairs. And I'm going to put some singlets. Okay, So I can write a constructor ground-state where I pair these two spins, pair these two spins. Or if I want, I could do it on the other type of sites. Okay. And the question is which it is, okay, which ground state is this? And this ground state actually breaks translation symmetry because it picked some of the, selected some of the bonds, although these bonds are equivalent. So what the ground state actually is, is a superposition of these two possibilities in very, very simple terms. Okay? And what happens in a spin chain like this? The ground state of the thing is what we call a macroscopic singlet. So instead of entangling two spins, two-by-two, you entangle all the spins with each other in something that we call the quantum spin liquid. It does not break any symmetry. In particularly there is no, there is no direction for the spins. Wherever you are in that chain, you cannot tell where you are. So there's translation symmetry. So this is the liquid does not break any asymmetry, but it's a highly entangled state of matter. There are correlations between the spins and these coalitions are very important. If you look at the system closely, you would realize that at short distances the spins are actually almost antiferromagnetic, antiferromagnetic correlated. So locally it kind of looks like this, but at long distance it's disordered like in the liquid. So that's one example of what we call a quantum spin liquid and we know it exactly because we can solve it exactly. Okay? One of the interesting aspect of this quantum spin liquid, no, I am removing this entangled picture, which is the right picture. And I'm going to the local physics, which is antiferromagnetic at local scales. And I'm, I'm plotting the system like this and then I'm asking what are the excitations? Okay? So physicists love to steady systems through the excitation. So what is the excitation of the system while you have one spin here? And what can you do? Well, you can flip it. Okay, so that's an elementary excitation of a magnetic system. And it turns out in this entangled ground state, when you flip one spin, you see you're creating to domain wall, so defects. And you can take these two domain walls and you can separate them independently. They behave independently in the system. And this is an example of something we call fractionalization. So I created an excitation that has ethical one because I started from a spin plus minus half and I bring it to spin minus 1.5. So I have a data ethical one, excitation, but I've fractionalized this excitation into two sub particles that have spin half. Okay? So if you go into the theory of this, you realize that this excitations, we call them spin-offs. They are fermionic, they behave like Fermions, although the initial excitation was a spin one, so it behaves like a boson. So this is an example of what we call fractionalization. And so the beauty of all of this and the message here is that we have a way to know if a system is quantum entangled. It is quantum entangled if it exhibits fractional excitations. Okay, So that's the, that's the message from this. And now the question is. Can I measure this fractional excitations? Before I do this, let me just give you an example of something more simple that you may be more used to. And that's the ferromagnet. So let's consider a ferromagnet. All the spins are aligned and I excited, I also flip has been, but now my flip spin propagates just as a coherent particle. It does not fractionalized into domain walls. Why? Because if I separate these two orange bars here, you would get two spins down, three spins down, so that cost you more energy. So this does not happen. So in a ferromagnet, the excitations are just this stuff propagating and this is what we call the spin wave. This is a Fourier transform of a flip space. Okay, good. So now how do we, you know? So again, the message is that we have, we cannot tell for sure if a system is quantum entangled, but what we can do is measure its excitations. And from the understanding of the excitations, are the fractional like here or are they integer like here? We can tell if the system is entangled. So that's what we're going to do now. Okay? So how do we do this, or do we characterize spin liquids? And my technique involves something called neutron scattering. So you don't treat fire with fire, twitch spins with Spence. That's the idea here. So one of the beauty with neutron scattering in many regards resembles X-ray diffraction. So you prepare a beam of particles which are Waves by quantum mechanics and you shine them on your sample. But the beauty is that the neutron itself as a spin half degree of freedom. So through the spin of the neutron that can interact with the spin of the sample. We can understand with the spins are doing in the system. Okay? So scattering experiment is simple. You prepare, well, you prepare a beam of particles. They have a well-defined momentum, well-defined energy, well-defined spin, or as good as your instrument can prepare such things. You scatter it on the sample and then the, the neutron will be deflected. It will deposit momentum, energy and spin in the sample. And then you can measure the resulting pattern of diffraction from, from, from the neutron be. So we can formalize this and we can try to understand a little bit the theory of neutron scattering without going in details which are not necessary for this talk. What we measure in the detector, the cross section is proportional up to some terms that are just geometric in nature. Something we call the dynamic structure factor S of Q and omega. And you may want to, what is S of q and omega? Well, this is that quantity here. This is the Fourier transform in time and space of coalitions between space. So imagine you have the movie of what all the spins are doing while you Fourier transform it in time and space. And that's what we get for neutron scattering. So my job and my students job is to disentangle this Fourier transform to understand what the spins are doing in real space, in real time, in very simple terms. Okay? So the series well established and all of this works great. So let me give you an example of how a neutron scattering instrument looks like. So this is just a schematic here of an instrument at Oak Ridge National Lab. And this is what looks the most like an x-ray refractometer. So you have neutron source, which is a nuclear reactor. And then we prepare a beam of monochromatic, where we have a beam of neutron that comes, Here's the monochrome matter, so it prepares a well-defined wavelength. This neutrons impinge on the sample or sample scatters the neutron and are deflected at many different angles. They may lose or gain energy, so they have a different wavelengths. So here in this bank here we have analyzers like in a Raman spectrometer for instance. And we can measure as a function of the scattering angle and the energy loss, the scattering. So this is one type of instrument. This type of instrument is not very efficient because we, out of all the neutrons that are scattered by the sample, we only detect a small, small solid angle if you wish. So the new generation of instruments that we are using rely on something called the time-of-flight technique. So, so what we're trying to do is to remove the analyzers. And in order to remove the analyzers and still know the energy of the neutrons, we rely on the time-of-flight. So the beam of neutrons, instead of being continuous, it's passed. So it's coming at a certain frequency, which is 60 hertz, impinges on the sample. And then the sample will scatter the neutrons in a large area detector, which is of the order of five meter by five meter, millions of pixels. Okay? So like this, we can measure in some way. It's a polyline detection system, okay? And because we do time-of-flight, we can simply measure as a function of time to reconstruct the energy of the neutrons that are impinging on the, on the, on the detector. So this is a very efficient way to do neutron scattering. Ok. So time-of-flight, time-of-flight, neutron scattering. Ok, so first, finally some data that I took during my PhD on a very simple system. So this is copper sulfate. Copper sulfate is in some approximation at very low temperature, 100 milli kelvin. It's a spin chain. Okay, and what we do here is we measure the excitations of that's been chain. Remember that I told you they should be fractional. I measure them as a function of momentum transfer. So the scattering angle along the chains and energy, and you see the energy is very small and below one MeV. And what I see is this, the color here encodes the scattering. So if it's red, it's very intense. If it's blue, there is no scattering, and so on and so forth. And what you see is something that looks like a sine wave here, but there's a continuum of excitations that lives above this thing. And this continuum of excitation is the signature of fractional excitations. So this experiment proved that this material at low temperature as fractional excitations and as a proxy, as an entangled ground state. But to be sure that this is the case, we did something that was very useful in this material. We apply a magnetic field. And because the interactions are so weak in the system with a 5 Tesla magnetic field, you can completely transform the system from an anti ferromagnet to a ferromagnet. And I told you in a ferromagnet, I don't have entanglement. I don't have fractional excitation, I just have spin waves. And indeed you see the spectrum is completely transform when I apply the magnetic field. And now you see that for one value of wave vector Av1 energy, this is exactly a spin wave or it's the bend structure of the magnet if you wish. Okay? In this experiment, prove that you can tune from a quantum entangled ground state to product state of classical state by using the magnetic field. And so these types of experiments after, so I was not the first to do this, but I was the first to do in a single material, the change of magnetic field like this. And so this experiment has become what people are looking for is the fractional excitation. They are looking for this continuum of excitations in materials to prove that they are entangled. Okay? So, so the picture that you should remember is a magnetic excited, traditional magnetic excitation is just a spin flip. It corresponds to all this has been processing and it leads to bands. This in the scattering and fractional excitations like spin-offs, they correspond to continuum. Good, So just to convince you, here's another example that I worked on as a student. It's not a chain now, but it's the square lattice, the square lattice antiferromagnetic. It has this kind of neo state. And if you measure the magnetic excitations in the first Brillouin zone as a function of momentum and energy, what you see is a well-defined, nicely defined branches. So it's a nice dispersion curve. This system is not entangled. There's just spin wave excitations and it behaves as we expect. So something is very special in that material and that's the 1D, the fact that it's one-dimensional. Got. So one thing I didn't tell you and that I can have head from this is that neutron scattering can be a huge pain for a reason, which is that this number here that relates the cross section to the theory or to the dynamic structure factor. That number is extremely small. The neutron scattering cross section is extremely small. So x-rays interact with materials through the electrons, scattering is strong, but neutrons interact as a dipole-dipole interaction. So the scattering is very, very weak. And on neutron sources comparatively to X-ray scattering sources are also very weak. So, so there's no way around it. Rather you make it more intense neutron source or you bring more material to the B. Okay? And here versus the example of we bring more material to the beam. So these are single crystals of the materials of interests that we grew in different ways. And for instance, the copper sulfate sample I showed you was a five-point five grams of single crystal. Okay. So that's as far as I know, the biggest copper sulfate when you can actually make them very, very, very big. Even high school students can do this, but it's actually heavy water crystal because hydrogen absorbs neutrons. So anyway, these are examples of materials we've been working on in the lab. And one example here, recently a student of my Joseon Bye come on making samples of a simple material FEA to any went from doing CBT growth in the lab that yield milligram type samples to a five grand Bridgeman grown single crystal that we grew at Johns Hopkins. And so in my lab we're always concerned about making of samples bigger. Okay, So that's, that's because the neutrons interact so weakly with the system. Okay, so that's one way. And that's a picture of the saying. So of course we interact with IN and the MCF to characterize on materials. And we have things that look like chemistry in the lab to make these systems, right? So the other way is to increase the neutron flux. Okay? So depend on much money you have. You can do this, which is going to cost you 50 K per sample, the time investment of people. Or you make your neutron source more intense. And that's going to be a $1 billion investment. And that type of investment is ongoing at the Department of Energy is Oak Ridge National Lab. So some of the data I showed you was measured on despoliation source at Oakridge that opened in 2007. So let me just explain. This works very briefly. We take some protons, we accelerate them close to the speed of light. We bunch them together and at a frequency of 60 hertz, we smash them in a bucket of liquid mercury. When that bucket of liquid mercury gets excited. Neutrons are emitted from the mercury in a pulse fashion. And then we channel this, this neutrons two different beam lines. Okay? So that's been working pretty well. But now we're involved in a project that we call the second target station. And what we will do is one proton out of six will be deflected to new building with a new source and a new set of 20 instruments or something like this. So the thing that is amazing about this project of new neutron source is that, so when the neutrons are produced here, they have a lot of energy and we need to moderate them. So like in a nuclear reactor, we need to move their energy from the MeV with a big M, two MeV was small. And there's been a lot of advances in designing moderators that allow us to keep the flux of neutrons. And it is projected that at the second target station, the flux of cold neutrons. So five Angstrom wavelength, the neutrons that I care for my type of problems, low energy magnetic problems. This flux, combined with the instruments being better, might be as much as a factor 100. So now instead of bringing, bringing one gram Crystal, I may be able to bring 10 milligram crystal. And if you know the difference between one gram crystalline 10 milligram crystal, it's the day and night in terms of synthesis. So we believe that with the new neutron source will be able to look at samples as they arrive on the, on the market. Some of these crystals, you know, it took us years to grow in particularly this one took years to grow. And so by the time we did the experiment, nobody cared that at that point here is not entirely true, but, okay, And so another thing we can do, just very briefly. So because that sources at 60 hertz, so 11 over 60 sec, every one of us 60 seconds, there's a new pulse of neutron coming in, but that neutron source will be at 10 hertz. So there is much more time between pulses. And so what we will do at this saying is, instead of sending one monochromatic beam of neutrons, we will send several wavelength. And in the time we have between tosses, we can analyze multiple wavelengths. So it has a multispectral component to it. So at the same time, we will increase the flux, but we will measure different wavelengths at the same time. And we believe that's going to be very useful to understand some of the systems. So stay tuned. 2032, $1.5 billion. Talk to your congress person. Okay? At least we were already planning, we're already designing instruments and I'm involved in one project called Chess. This is an instrument by gaba yearly salary, which is one of the spectrometer that will be there at Oakridge spallation second target stations. Good. So let me finish off with the future and the things we'd like to do, the things we'd like to study if we have this amazing nutrient source. So before I do this, we're going to go back to our pension problem and we're going to ask a simple question, which is what if I don't have a spin half degree of freedom? But imagine ever spin one degree of freedom, I add one electron. So first of all, the material that will produce such a chain cannot be made of copper. Why? Because there's one electron in the orbital of carbon. So we need to move to something else, for instance, nickel, where you have two orbitals that have the same energy and I can put two electrons in it, so I will spin one system. Okay? Now, you can just imagine it's the same model as before, except it's made, we spent one. And we call this model the Haldane chain. And how they got the Nobel Prize for understanding that and other aspects of that system. So let me just show you what's different. So I'm going to do a little trick that was invented by Affleck leap Kennedy and the psyche, which is to add a non-physical part of this Hamiltonian. But that don't, don't worry too much about this. What I'm gonna do here is, okay, Instead of having a spin one, spin half, spin one. So I'm going to divide my spin one into spin-offs at every site. So you see every side of that chain, this pin, for instance, has been divided in one spin half here and one spin out. And I told you when I have spin half, what I want to do is create singlets out of them. So here I'm creating singlets between the spin house. But you see the beauty of this model is that the singlet involves 1.551 spin from that site in 1.5 spin from this other site. So we are constructing a ground state now that entangled two paths of a spin, one from two different sides. And we create a ground-state like this. That is exactly that. It's actually the ground state of the system. It's exact. And it has something called topological order. So that's a little bit difficult to understand, but formally, but just imagine that that chain as finite length. Okay? Just imagine to finite lens system. You see there is one lonely spin half at the end and one lonely spin half at the end. That has not been entangled because there's nobody to untangle it with. So this finite length, how they in chain as singlets in the bulk. And to break a singlet, you need to pay an energy which is j. So the bulk is gapped. But at the edge of the system there is a spin half degree of freedom that if I apply a magnetic field, for instance, will be able to orient in the magnetic field. So the edges of the system or gap plus. So this is actually the first example of a topological state of matter where the bulk is gapped and the edges are gap plus. And for this The way this was not written down the first time like this. This was written down in terms of field theory. But for this and other contributions, how they got the Nobel Prize a few, a few years ago for understanding this kind of phenomenon. And now the way we understand this is that this measure on this, this dangling spins at the end of the species is actually something we can measure on a Fermions. They have a special property. They are their own anti-particle. And because they are their own anti-particle, they can be used for quantum computation. So I will not go into details because I don't actually know much about how we would do this. But they are very exciting from that perspective. But one problem, at least as far as I'm concerned, as a scatter that sees things in reciprocal space. This physics is addressed in local space, in real space, this is a local problem. This is not a global problem in reciprocal space. This is something that happens at the edge. So to fully understand the systems, we need to move to real space probe. So the first thing you might say is let's do scanning tunneling microscope. But the systems are insulating so you cannot tunnels through them. So one of the emerging technique is nitrogen vacancies sensing. So you put a small cube it on an AFM tip and you can go and hope to go and scan this. And so that's something I'm quite excited about for the future. And I'm not doing this, but, but others are doing this. Okay? So now this is 1D and this is known since the 1980s and we don't have a quantum computer yet. And the reason for this is that 1D is really special. And the question is, can this happen in higher dimensions? And until recently, we believed it cannot happen in higher dimensions. But emerged an ID from the physicist Alexander IETF that is revolutionary in many ways because kit, I have found an exact, so this is also an example of a form of quantum liquid. Kitty I found an exact quantum liquid in two-dimensions. So let me try to explain how this works very briefly. This is the end of the talk, so we can go in the weeds here. Okay? So, so imagine my magnet is not a chain, but imagine it's a honeycomb lattice. And we have a lot of magnetic systems that can be on the honeycomb lattice. And what could I have invented? So it's also a spin half system, but what IETF invented is a very special type of interaction that is not Heisenberg. So usually if you have two spins, the energy of that bond, for instance, is going to be S dot S. So it's going to be the dot product between two spins. But Kate, I have created an Hamiltonian that is similarly and physical, where the blue bonds connect only the x component of the spins. The red bond on the z-component, in the green bond on, in the y-component. So it's some kind of Ising system that is bombed dependent. It's a very weird Hamiltonian. Okay? And it turns out we can realize this Hamiltonian. We can make materials that actually have this property. Though, the way to understand this is that we need spin orbit coupling. We need the spins to know about the lattice. So there needs to be an amount of spin, a bit couplet. So we need to move away from the transition metals that typically small spin orbit coupling to, for instance, ruthenium, Iridium or praseodymium four plus we have a rule here, works in LA peer's lab on making presently num four plus systems because of their spin up a bit coupling properties. Okay? And it turns out that if you couple some of these ion in a certain geometry in a crystal, you may end up with this bond dependent interactions. And we have a few specialist on campus including the new theorist, Itamar kimchi, who kind of was at the leading edge of understanding the connection between the strange Hamiltonian and materials. And why does this work? What actually happens? Okay, So this is the revolutionary ID by Gita. If you take this Hamiltonian and at each site where you have all your spin half, I'm going to fractionalized my spin half into four types of fermions. Okay, this is some weird ID. So we're going to fractional is in four types of fermions. And you see, for instance here, so that site as the orange fermion that is at the middle and a red, a green and a blue, that blue fermion. I'm going to pair with another blue, that green fermion going to pair with another green. So I'm going to create the singlets okay, in the system. And I can now going to remove them. And I'm left with, at each site one fermion here that leaves I'm dancing. And it turns out this fermions, or also measure on our fermions, they are their own anti-particles. And we can actually propagate them and move them, move them in the crystal. So let me rewind here a little bit by doing this kind of, okay, this is a cartoon of what was done with feel theory techniques. Okay? But she tire found an exactly solvable quantum spin liquid for this Hamiltonian, which, which was completely unexpected in physics, usually we don't have exactly solvable problems. This is an exactly solvable thing. So it's telling you quantum spin liquid exist, we can prove it. Okay? Now do the other realizing material is another story, okay, but so we use this thing and then you realize, oh, you are left with some fermions are localized and some fermions are itinerant. And we can use this fermions in principle. To do all sorts of stuff like quantum computation. But also we can probably detect them using neutrons or photons or by directly coupling them indirectly to two phones for instance. And recently. So the question is with materials, do that in recently, a material emerge that is called deuterium trichloride that you can grow as relatively large single crystals. And it is believed that ruthenium trichloride realized is that Hamiltonian. And they've even been neutron scattering experiments on that material by the group at Oakridge colleagues of ours. And they found some scattering signal that is evocative of the presence of itinerant measure antifermions in this material. However, the story's a little bit more complicated. Conferences are full of people arguing about this, so I will not, I will not tell you that this happened. We did not find the tie of quantum liquid, but we have IDs of simple materials that may realize this. And here you see ruthenium as one of the nice property. We can also use president four plus four plus this many materials candidate. So here we are in a regime where there's a beautiful theoretical ID and people are trying to find the materials that we'll realize that ID. And with neutron scattering, we can try to be a little bit the police here and say no, you don't have fractional excitations, you do a fractional excitations, you Evan and tangles ground state or you don't. But before we do this, we need large crystals. And if we don't get large crystals, we need to wait for the second target station in 2032 to do that. All right. I will I'm about done here. So good. So this is pictures at this point. Of course, things are a bit more complicated and I'm happy to discuss and engage some of the details. But let me just conclude here and talk just very briefly about the future challenges. So research we are doing and what I've presented here, in some sense, it works like this. We want to find quantum spin liquids. And here at Georgia Tech we have people in material science, chemistry, or in my lab that make new materials. We can investigate them with spectroscopy such as neutron spectroscopy or optics. And then we can couple this to theory. So right now in my lab, we are engaged in this feedback loop between making the materials, understanding the spectroscopy, understanding the theory, and trying to give feedback and discover new things. Ultimately, what this will produce is we will satisfy in this material we have fractional excitations. So what, what can we do from this, okay, And why, why it did not happen yet? So one of the thing that is emerging and that I feel is very important is that some of these phenomena are really best understood in real space and in the time domain. Exactly we're scattering technique like mine is not adequate because we're in momentum space and energy space. So we need to couple these discoveries with real space sensing of these materials. And I think that's a very large area that is emerging. And that's the example here of this NV center qubit that is on the diamond at the bottom of that AFM that can be used to sense the material and go and measure this excitations that are localized in the system. So that's one thing. So that's to help in the discovery. And the other thing is, once we have them, What can we do? Can we make devices out of these materials that have this fractional excitations. One of the biggest challenge, all the materials I talked about insulators. So what are you going to do? You're going to put some gates on it and you're going to apply a difference of potential is not going to do much, okay, maybe you electrostatically will change a little bit the crystal field. But so one of the big challenge and what a lot of people are thinking about how we use the spin liquids in devices. So here for example, this is from the paper or just an LLC at Caltech, where what you do is you create an interface between your spin liquid insulator and maybe a quantum whole state. And then you will be able to transfer the entangled nature of your exotic particles here to the quantum Hall system that is metallic and then to gate. And then you will probably be able to interrogate and do something to the system. But this is, this is a conceptual thing. Okay? So what I see a huge challenge for the future is doing the translational research. How do we go from this physics discovery to something that may be integrated in a device, okay? And people are thinking about a lot of exotic ideas. So of course you could use light to couple to the spin liquid. You can also use thermal transport. So although the system is electrically insulating, it is actually thermally conducting. And so you may use IDs of thermal transport to move to, to, to interrogate this quantum system. But we don't have this yet, so don't get too excited. The clean room will not suddenly get booked with retaining them trichloride people, although in some places they are massively investing in function analyzing some of these materials, although it's not completely clear yet. If they are fractional, if they are fractional excitations. So with this, That's all I have and I'm happy to take your questions. We have time for a few questions. Here in the room. Isn't it? Just sort of bring like when you talk about quantum spin liquid drain. And then good, would you consider the transition from a paramagnetic state to state as an actual phase transition begins not necessarily breaking any symmetry, right? What is a country that has a phase transition? Yes or no? But that's a great question. So, so maybe I go back to the, to the very beginning. E S, either the better cartoon in another, in another talk. So what's the difference between a liquid and a gas? Okay? So in a gas, the positions of the atoms are uncorrelated and in the liquid they become correlated. Okay? So you may imagine the same happens in the spin system. So you have a traditional tarmac that the spins are fluctuating, fluctuating thermally, completely decorrelated. You call the system, it becomes a classic, what I would call a classical spin liquid. The equivalent of this, right? So the spin directions are correlated, still fluctuating but non entangled. And as I go to the lowest temperature, then there should be a transformation that is not a phase transition, where there is coherence and entanglement that sets in most of the time materials bracket transition. There is a little bit something you've not considered the new Hamiltonian that actually breaks the symmetry and the system orders. So that's why it's so difficult to find them. But one of the key question, the theory of this is how do you go from classical to quantum? What are the phenomena that are taking place? Or do you send HBr to 0? And some of the things we're doing on F2 and the SUN magnets at this, going towards this, which is what happens when, you know, you, you thermally excited magnet. And how is the h bar? Where's the edge bar going? We're always the quantum mechanics going away. So this is a, this is a very important question. I don't have an answer to this. This is actually one of the most important thing. How do you go from a quantum system to classical system? How does coherence and entanglement vanish to be a product stayed at high temperature. And it will depend on the details. But this is exactly the this is what we should be working on. Thanks, Martin. Are there any other Thank you very much for your talk. I'm curious and I don't have the right words for this. But when you're looking at the 1D chain, what, why doesn't the whole systems which, what keeps those kind of domain walls from propagating throughout the rest of the material in the ferromagnetic case. Okay? Yep. And the antiferromagnetic case or in the anti Ferro that they do propagate, right? But what keeps the entire system from switching? Why does a okay? So that's, that's, that's a great question. So nothing prevents it. It's the cartoon that is wrong. So I'm doing a cartoon here when I'm assuming that I have an antiferromagnetic state, but I'm also telling you is a liquid so it should not break. So you should imagine that this spins actually fluctuating in time. But locally, I'm making a snapshot of the system in locally it is antiferromagnetic. Locally I create the thing and these two domain walls. But then you're right that the overall direction and the whole thing vanishes at long times. So we should really imagined that this system is, is, is fluctuating. So this is, this cartoon is wrong. I have no choice. Okay, I have to give an idea of what is going on in the ferromagnet, then there's no problem. This is a broken symmetry state and everything and behaves traditionally. Anything else? If not, let's thank Martin. Thank you, everyone. Excellent seminar.