 Это круто быть снова в этом прекрасном месте. Спасибо за организаторами. И т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. т.е. Т.е. в первую очередь, мы знаем, что есть много теорий и много экспериментальных экземплов рисунокulated excitations of low-dimensional systems where fractionalized excitations exceed. Fractionalized excitations are excitations with fractional quantum number of an electron. В данном случае, в одном из системы, мы можем получить эксцитации с качей E, с качей 0, которые обычно называют полонами, или эксцитации с качей 1,5, качей 0, называемой спинами. Так что, мы не имеем еще редко, лабораторий, экспериментальный эксперимент, существующий из таких эксцитаций в высоких дименсиях, но у нас есть, у нас есть определенные, скажем, эксцитационные модели. Это неизвестные гейтсюреты, в которых такие эксцитации предназначены существовать. Теперь, что случится, если электроны создают бонусные статусы, то это так, как в фракциональной партии, а потом, в фракциональной статусе, это возможно, именно когда эти бонусные статусы создают бонусные статусы, потом они будут фракциональными статусами. Это концерт. Теперь, в этой статусе, которая с помощью нашего работа, с пирскомомом и одетия по анегратию, я will discuss a particular model where such fractionalized order can be realized. It's a three-dimensional conda lattice, where we manage to treat the strongest interactions exactly and basically derive this fractionalized order under a complete control. And this fractionalized order will be a condensation of spin one-half, charge E boson. Here is the plan of the talk. I will describe to you our model. It's a conda lattice where conduction is called a calcule to localized moments. So you can think about these localized moments coming from flat bands. That's where they always come from in conda lattices. And it is essential that in these models the spins interact between themselves and these interactions are strong. They form a spin liquid and we describe them essentially by an exactly solvable model, which is called the Yawly spin liquid model. I will describe to you this model in detail. And this spin liquid has fractionalized excitations, which create bound states with the conduction electrons. The bound states condense and the result will be a corno-copy of interesting features. The broken symmetry states will be a pair density wave. The order parameter will also break the time reversal and the pairing amplitude will have a piece, which is odd in frequency, so odd frequency pairing. And of course, as I mentioned, this is an example of an order parameter fractionalization. So the results in nutshell are here. So as I said, the essential ingredient of our model is the Yawly spin liquid. In this spin liquid there are two types of excitations. There are propagating excitations, there are spin-1, myaranofermions, and there are non-propagating excitations, which are static non-confining Z2GHP. The model, as you will see, is somewhat similar to the famous China model, but there is a very important difference. Namely, the local spin-1.5 is local in the myaranoferm. So unlike in the China model, where in order to flip the spin, you need to create a gap-wise, here you will need to do this. The myaranos here are gapless, and therefore the spin excitations of this spin liquid will be also gapless and incoherent. And now the exchange interaction with the conduction electron creates bound states of electrons and this fractionalized excitations that it dynamically generates a hybridization matrix element between conduction electrons, which carries spin-1.5 and the myaranos. That's essentially the main ingredient of our work. So local spins fuse with the conduction electrons and produce a bosonic field, spin-1.5 charge E, and neutral myaranofermion. And in the low temperature state, the alpha spin field condenses. This is the fractionalized order. Now, basically, yes, these are the main results. Now I will describe the details and first of all about the gaoli model. So this is the Hamiltonian. So you see on each side, here for simplicity, I give a cartoon of this model on the honeycombe lattice. This is not the lattice we will use, but this model is exactly soable on any lattice with coordination number three. So on each side of a lattice, there are two spins. Well, this one will be spin-1.5 D, D, D, D, described by this sigma Pauli matrices, and there is SUDE spin-1.5 D, D, described by Pauli matrices tau. And this model was introduced by these two gentlemen, Яуэн Ли в 2011 году, и exact solution goes along the lines similar to how the Kigitaif model is solved, namely through refermination. You can faithfully reproduce the commutation relations of the Pauli matrices, introducing six Myrano-Fermians, Psi and B, subject to this constraint, and the constraint commutes with the Hamiltonian. When we substitute these expressions into the Yawli Hamiltonian, Probably I did not emphasize that this tau matrices interact like in the Kigitaif model. So, along one bond it will be tau x, tau x, along another bond it's tau y, tau y, along the third bond tau z, tau z, tau z. But at the Cigba matrices interact like in the Heisenberg model, with the issue of symmetry. When you substitute these expressions for Cigba tau into this Hamiltonian, you get this form where these products of B, Myrano-Fermians, on every link, commute with each other and with the Hamiltonian. So, essentially we get the model of non-interacting fermions, subject to a static Z2 field on each link. So, on each link we have two fields which can be equal to plus minus one. And, of course, there are two kinds of excitations as you may understand the propagating Myrano-Fermians and these fluxes of the Z2 gauge field started, they don't propagate. In order to create a flux, it costs energy and in the three-dimensional example I will be using, there will be a finite temperature phase transition below which these fluxes are essentially confined and rare. Let me say a few words about this confinement, probably many of you have heard about this. In the two-dimensional key, a type model, when we flip one bond, a sign of one bond, we create two Zs into fluxes and neighboring плакет, but it costs a finite energy to separate these fluxes as far as you want because by flipping these bonds we don't disturb neighboring плакет, but in three-dimensional lattice, this is no longer the case because, as you can see from this picture, for example, by flipping one bond, we disturb not two but several neighboring plakets and to perform the same operation would cost you the energy proportional to the distance between the fluxes. So, in three-dimensions fluxes can find and there is a finite temperature confinement, the confinement transition and we will assume that we operated at temperatures below this three-dimensional, as in like the transition and we will not worry about this Z, Z2 gauge field at all. Now, this is our three-dimensional lattice. This is the so-called hyperactogonal lattice, which is basically a BCC lattice with four sides in the unit cell. Why we have chosen this one? Because it turns out that the Myeran fermions on this hyperactogonal lattice have a firmness here. So, the spectrum is, there are four bands here and one of them crosses the zero, there is no chemical potential for Myeran fermions and there is a single fermi surface in the brilliant zone. This is B, B, B, because Myeran fermion is a real particle and the creation operator at K is equal to the annihilation operator minus K. So, they occupy the equivalent to the Dirac fermions occupying half of the brilliant zone only. Now, yes, yes, yes. No, no, just assume. This is an equivalent. Now, I said Myeran fermions are like Dirac fermions in half of the brilliant zone. So, the other half is the Gauss. Now, the most difficult status taken and now we can construct the condolences and we do it in the way most favorable for the fractionalized order parameter. So, we look at the, we consider conduction electrons on the same, hoping on the same lattice. So, they have at half feeling they will have exactly the same fermi surface as the Myeran fermions, but the only difference that it is, the electronic fermi surface is centered around the gamma point. And the Myeran centered around the P, P, P, P point in the brilliant zone. And this will be important for the paired estimator. Now, the interaction is between spins of conduction electrons and physical spins, sigma of the Yawli model. And, as I said, the nesting between the two fermi surfaces encourages creation of bound states between Myeran and conduction electrons. You, you, you, you, you, you who can write down this interaction in such a form, that it will be a product of two, of two other parameters and the, the, the, the HECOPOLITIES, the Hubbard-Straton rich transformation, but equally well. You, you can sum the leading logarithmic, logarithmic diagrams in the expansion in the KONDA coupling. So, so, so, sorry, the investing leads to instability and there is an interesting, interesting feature that there is a mismatch between the quantum numbers of Myeran and conduction electrons. There are three Myeraners and there are two, two Dirac fermions equivalent to four Myeraners. The, the, therefore, there is a mismatch in quantum numbers and when they hybridize, one electronic mode will be left ungapped. So the, the, the, this is the spectrum, be, be, be, below the single excitation spectrum, be, below the, below the phase transition. The, the back bent Myeraners and the spin liquid Myeraners are all hybridized with each other and one, one, one conduction mode is left untouched. So, what, what is the, the spin of the alpha is not the two gauge invariant. So, in order to discuss rigorously the fractionalized order, you need to look for, for, for the gauge invariant quantities and one of these gauge invariant quantities is the anomalous part of the electron self-energy. So, how, how it will look like? Well, the electron enters into the spin, spin liquid leaving behind its charge and it can re, re emerge back from the spin liquid either as a hole or as an electron. And the, this electronic self-energy was its normal and anomalous part z, z2 gauge invariant and you, you, you, you, you who see you can make z2 gauge invariant or the parameters as 3, 3, 4, 5. 3, 3 components of the mutually perpendicular unit vectors, but they are actually made of these, it created as far apart as you, as you like. This, this, this, this is the best illustration of, of this order fractionalization. Again, if you don't take the fluctuations into account the anomalous part of the electron self-energy. Ландем. Ландем. The anomalous part of the electron self-energy is here and as I mentioned, due to the fact that Fermi surface of electrons and the Fermi surface of myravis are situated at the different parts of the brilliant zone. Д, this D with vectors will change the, that direction from side to side in the unit cell and that's essentially why this superconductor is also a pair density way. Дело в том, что мы берем чачу, и в магнитическом филе, может быть, H over E, И вот это, это, это еще один distinct feature of this phase. И я думаю, что я сказал все, что я хотел. By the emergent gauge fields of the underlying spin UV. You having a logarithmic problem because you fine tune the family service of the conduction electrons. yes Is the interaction that you then looking at, is the only symmetry allowed interaction before, is there any need to look at other channels, where you would have to look what are the competing logs. And this is actually the natural instability. Я не думаю так. Потому что это единственная интервью. Вы можете поделиться, что это инвериант с СУ2. Я вижу. Это очень удивительно, да? Нет. Не в интервью. Не в интервью. Вы не имеете еще другого константинга. В вопросе, есть ли есть permission, в какой-то низкой энергии, чтобы иметь еще другого константинга. Вы можете поделиться? Это вопрос. В разных моделях, где, я думаю, вы можете. Ну, ну, конечно, мы делаем бэст для конструкции в тактический способ. Окей. Вы говорите, что у вас H over E, вы исключаете H over 2E, что это? Нет, нет. Вы не можете. Нет, нет. Они могут быть двоими. И, в принципе, они будут вынуждены с энергетиками из ваших моделей, которые будут появиться. Я думаю, мы можем выяснить, что в магнитических моделях, будет х over 2E, вот это. Но когда вы увеличите магнитический модель, будет х over E. Таким образом, вы знаете, чтобы у вас х over E, вы тоже нужно производить бонтфлип. Вайсерно. Да. Поехали. Прекратим вопрос. Я хочу понимать, как в фазе вы получите после конденсации фрагменты. В результате в фазе есть ли это фрагменты или нет? Да, в принципе. У меня есть один гаприсмайон, гаприсмайон, у меня есть гейшфилл, лето-гейшфилл. Ну, в лето-гейшфилле эти эксиситацииslow гольдстон или ещё один параметр коллективных эксиситаций и гипсисмайон, гаприсмайон, в которую что-то не за все интернете Электроны могут создать один статус с майораном, потому что это не так много в квантомном количестве. Вы выгадываете обоих другом? Они, они... Вы в три... Вы в три дименции... И они на религии... Вы выгадываете обоих другим другом? Нет, я mean... В отличие, этоactive is 재орashionable. ... again Which excitations do you mean? The below the cloth transition You have Габт, Боголюбов, Твозей, Папико, Тихичев, Фермиан, Магайарана Фермиан. И Габлес, Майаран. Они все... Есть какие-то резидиальные интеракции на этом сочетании. И Кьюбут Хефеном, и Денис Суперканда. Покажем вам, Ви, формула для Ви, для вашей биленеи. Эта? Нет, для Ви, в том числе электронных и аэронных. Вот это. Ага. Так, это укрепит 1,5 спин. Да. Так, ты притереваешь спин ротационный симметрии, спонсорный стиль. Это притеревать спин ротационный стиль. Да, абсолютно правильно. Я говорю. Опять-таки, вы видите три вектора. Так, Ди-1, ну, они все притеревают в реверсии.