# RAQIS'20: Titles and abstracts

AVAN Jean     Classical r-matrix structure for the complex sine Gordon model.
The complete algebraic framework underlying the r-matrix structure associated to the classical complex sine Gordon model is unraveled.

BABENKO Constantin     One point functions of fermionic operators in the Super Sine Gordon model.
We describe the integrable structure of the space of local operators for the supersymmetric sine-Gordon model. Namely, we conjecture that this space is created by acting on the primary fields by fermions and a Kac-Moody current. We proceed with the computation of the one-point functions. In the UV limit they are shown to agree with the alternative results obtained by solving the reflection relations.
Based on arXiv 1905.09602.

BELLIARD Samuel    Some recent advances in the Algebraic Bethe Ansatz
I will discuss a new way to calculate some scalar products from the algebraic Bethe ansatz point of view. In particular it allows to proves conjectures for a determinant form of the scalar product for models without U(1) symmetries such as the closed/open XXX spin chain.

BYKOV Dmitry    A new look at integrable sigma-models and their deformations.
I will show that integrable sigma-models with flag manifold target spaces, as well as their (trigonometric/elliptic) deformations, are chiral gauged bosonic Gross-Neveu systems. The interactions are polynomial, and the cancellation of chiral anomalies is related to the quantum integrability of the model. Ricci-flow properties of the models are easily established at one loop.

CANTINI Luigi    Boundary emptiness formation probabilities in the six-vertex model at Δ=1/2.
Since the seminal work of Razumov and Stroganov, we know that the ground state of the XXZ spin chain at Δ=1/2, for specific boundary conditions, displays a rich combinatorial content, several zero temperature correlation functions of this model have (conjectural, and sometimes proven) closed exact formulas, even at finite size, often involving enumerations of combinatorial objects such as Alternating Sign Matrices or Plane Partitions. In this talk, after briefly reviewing some of the relevant background, we shall present new results obtained in collaboration with C. Hagendorf and A. Morin-Duchesne, concerning the overlap of those ground states with particular factorized states. Such overlaps have a nice interpretation in terms of the six-vertex model on a semi-infinite cylinder with free boundary conditions, as the expectation value of a string of polarized edges at the edge of the cylinder.

CRAMPE Nicolas    Free-Fermion entanglement and Leonard pairs.
I study the entanglement entropy for free-Fermion model. I recall how it is related to the computation of the chopped correlation matrix. Then, I present the construction of the algebraic Heun operator which commutes with this correlation matrix and simplifies the computation of its eigenvalues. I show why the concept of Leonard pairs is important in this context.

FRASSEK Rouven     Non-compact spin chains, stochastic particle processes and hidden equilibrium.
I will discuss the relation between non-compact spin chains studied in high energy physics and the zero-range processes introduced by Sasamoto-Wadati, Povolotsky and Barraquand-Corwin. The main difference compared to the standard SSEP and ASEP is that in these models several particles can occupy one and the same site. For the models with symmetric hopping rates I will introduce integrable boundary conditions that are obtained from new solution to the boundary Yang-Baxter equation (K-matrix). Finally, I will present an explicit mapping of the open SSEP (and the non-compact model cousin) to equilibrium. It allows to obtain closed-form solutions of the probabilities in steady state and of k-point correlations functions.

GAMAYUN Oleksandr     Modeling finite entropy states with free fermions.
The behavior of dynamical correlation functions in one-dimensional quantum systems at zero temperature is now very well understood in terms of linear and non-linear Luttinger models. The "microscopic" justification of these models consists in exactly accounting for the soft-mode excitations around the vacuum state and at most a few high-energy excitations. At finite temperature, or more generically for finite entropy states, this direct approach is not strictly applicable due to the different structure of soft excitations. To address these issues we study asymptotic behavior of dynamic correlation functions in one-dimensional free fermion models. On the one hand, we obtain exact answers in terms of Fredholm determinants. On the other hand, based on "microscopic" numerical resummations, we develop a phenomenological approach that provides results depending only on the state-dependent dressing of the scattering phase. Our main example will be the correlation function ix XY model.

GÖHMANN Frank     Thermal form factor series for dynamical correlation functions of the XXZ chain in the antiferromagnetic massive regime.
We consider the longitudinal dynamical two-point function of the XXZ chain in the antiferromagnetic massive regime at zero temperature. It has a series representation originating from an expansion based on the form factors of the quantum transfer matrix of the model. The series sums up multiple integrals which can be interpreted in terms of multiple particle-hole excitations of the quantum transfer matrix. In previous related works the expressions for the form factor densities appearing under the integrals were either presented as multiple integrals or in terms of Fredholm determinants, even in the zero-temperature limit. Here we obtain a representation which, in the zero-temperature limit, involves only finite determinants of known special functions. This will facilitate its further analysis.

JIN Zizhuo Tony    Quantum exclusion processes.
Quantum exclusion processes constitute the natural generalization of classical exclusion processes such as SSEP, ASEP and so on to the quantum realm. Their equilibrium fluctuations entail a rich structure which accounts for the quantum nature of the problem. I will introduce such quantum exclusion processes and present recent results about their stationary properties.

KOZLOWSKI Karol     Convergence of the form factor series in the quantum Sinh-Gordon model in 1+1 dimensions.
I will discuss a technique allowing one to prove the convergence of form factor expansion in the case of the simple massive quantum integrable field theory: the Sinh-Gordon model.

LEVKOVICH-MASLYUK Fedor     Separated variables and scalar products at any rank.
I will present new results in the program of developing the separation of variables (SoV) approach for higher-rank integrable spin chains. This method is expected to be very powerful but until recently it has been little studied beyond the simplest rank-one cases. I will describe how to solve the longstanding problem of deriving the scalar product measure in separated variables for the su(N) and sl(N) models. The results are based on constructing the SoV basis for both bra and ket states. As a first application, I will derive new representations for a large class of form factors.

MALLICK Kirone     Exact solution for single-file diffusion.
A particle in a one-dimensional channel with excluded volume interaction displays anomalous diffusion with fluctuations scaling as t1/4 in the long time limit. This phenomenon, seen in various experimental situations, is called single-file diffusion.
In this talk, we shall present the exact formula for the distribution of a tracer and its large deviations in the one dimensional symmetric simple exclusion process, a pristine model for single-file diffusion, thus answering a problem that has eluded solution for decades.
We use the mathematical arsenal of integrable probabilities developed recently to solve the one-dimensional Kardar-Parisi-Zhang equation. Our results can be extended to situations where the system is far from equilibrium, leading to a Gallavotti-Cohen Fluctuation Relation and providing us with a highly nontrivial check of the Macroscopic Fluctuation Theory.
Joint work with Takashi Imamura (Chiba) and Tomohiro Sasamoto (Tokyo).

MEDENJAK Marko     Dissipative Bethe Ansatz: Exact Solutions of Quantum Many-Body Dynamics Under Loss.
I will discuss how to use Bethe Ansatz techniques for studying the properties of certain systems experiencing loss. This will allow us to obtain the Liouvillian spectrum of a wide range of experimentally relevant models. Following the general discussion, I will address different aspects of the XXZ spin chain experiencing loss at the single boundary.

NICCOLI Giuliano    New quantum separation of variables for higher rank models.
I will describe our new quantum separation of variables method (SoV) and I will consider as main example the rank 2 quantum integrable models. Our SoV is based exclusively on the quantum integrable structure of the analyzed models (i.e. their commuting conserved charges) to get their resolutions (spectrum and dynamics). This is a distinguishing feature of it; indeed, others methods rely on some set of additional requirements beyond integrability which may result in their reduced applicability. Our main aim is to establish a method allowing to put on the same footing the quantum integrability of a model and its effective solvability. Our SoV can be reduced to the Sklyanin's SoV, if this last one applies, while it is proven to hold for quantum integrable models for which Sklyanin's SoV or simple generalizations of it do not apply, e.g. the higher rank models. SoV does not make any Ansatz and then the completeness of the spectrum description is proven to be a built-in feature of it. It can be seen as the natural quantum analogue of the classical separation of variables in the Hamilton-Jacobi's theory, reducing multi-degrees of freedoms highly coupled spectral problems into independent one-degree of freedom ones. Then the transfer matrix wave functions are factorized into products of its eigenvalues (or of Baxter's Q-operator eigenvalues) and our SoV should universally lead to determinant representations of scalar products and even of form factors of local operators, as we have already proven for several models solved by it.

PROLHAC Sylvain    Riemann surfaces for KPZ fluctuations in finite volume.
The totally asymmetric simple exclusion process (TASEP) is a Markov process described at large scales by KPZ universality. Bethe ansatz for height fluctuations of TASEP with periodic boundary conditions is formulated in terms of meromorphic differentials on a compact Riemann surface, which converges in the KPZ regime to the infinite genus Riemann surface for half-integer polylogarithms. For specific initial condition, the probability of the height can be interpreted as a solution of the KdV equation assembling infinitely many solitons.

SANTACHIARA Raoul     New bootstrap solutions in two-dimensional percolation models.
A very long standing problem is the determination of the Conformal Field Theories that describe the continuum limit of non-local observables in two-dimensional statistical model such as the connectivity properties of random Potts clusters. In the last four years, a combination of 2D bootstrap approach, Temperlie-Lie representation theory and numerical simulations has unveiled crucial (and probably definitive) informations on these theories. In this talk I present the state of art of this project, the questions that are still open and, time allowing, some new lines of research.

SCHEHR Gregory    Non-interacting trapped fermions: from GUE to multi-critical matrix models.
I will discuss a system of N one-dimensional free fermions in the presence of a confining trap $V(x)$. For the harmonic trap $V(x) \propto x^2$ and at zero temperature, this system is intimately connected to random matrices belonging to the Gaussian Unitary Ensemble (GUE). In particular, the spatial density of fermions has, for large N, a finite support and it is given by the Wigner semi-circular law. Besides, close to the edges of the support, the spatial quantum fluctuations are described by the so-called Airy-Kernel, which plays an important role in random matrix theory. We will then focus on the joint statistics of the momenta, with a particular focus on the largest one $p_{\rm max}$. Again, for the harmonic trap, momenta and positions play a symmetric role and hence the joint statistics of momenta is identical to that of the positions. Here we show that novel momentum edge statistics'' emerge when the curvature of the potential vanishes, i.e. for "flat traps" near their minimum, with $V(x) \sim x^{2n}$ and $n>1$. These are based on generalisations of the Airy kernel that we obtain explicitly. The fluctuations of $p_{\rm max}$ are governed by new universal distributions determined from the $n$-th member of the second Painlevé hierarchy of non-linear differential equations, with connections to multi-critical random matrix models, which have appeared, in the past, in the string theory literature.

SERBAN Didina     The wave functions of the q-deformed Haldane-Shastry model.
The Haldane-Shastry chain is an unique example among the long-range integrable spin chains, since it possesses Yangian symmetry for any length. Although the construction of the eigenfunctions evades the usual Bethe Ansatz procedure, these can be found due to their relation with Jack polynomials. More than twenty years ago, a XXZ-like deformation of the Haldane-Shastry model was also proposed, where the Yangian symmetry is replaced by quantum affine symmetry. However, a similar construction for the (highest weight) eigenfunctions was not available until recently.
In the talk I will report on these results, obtained in collaboration with Jules Lamers and Vincent Pasquier, and I will comment on a set of open problems.

SZECSENYI Istvan M.     Entanglement Oscillations near a Quantum Critical Point.
We study the dynamics of entanglement in the scaling limit of the Ising spin chain in the presence of both a longitudinal and a transverse field. We show that the presence of bound states in the spectrum of the field theory leads to oscillations in the entanglement entropy and suppresses its linear growth on the time scales accessible to numerical simulations.

VIGNOLI Louis     Separation of variables bases for integrable Y(gl(M|N)) models .
I will show how to construct quantum Separation of Variables (SoV) bases for the fundamental inhomogeneous Y(gl(M|N)) supersymmetric integrable models with quasi-periodic twisted boundary conditions. The SoV basis are constructed by repeated action of the transfer matrix on a generic (co)vector. Diagonalizability and non-degeneracy of the spectrum of the twist matrix is sufficient to guarantee the same property for the transfer matrix. Eigenvalues are constrained to be solutions of a set of functional equations, namely the fusion relations, supplemented by an inner-boundary condition that arises from the representation theory of the underlying super-Yangian symmetry. Eigenvectors are characterized by their wave functions, which have a factorised form in the SoV basis.
As an application, I will treat the special case of the Y(gl(1|2)) model with particular boundary conditions and compare it to usual Bethe Ansatz approaches.
Ref : arXiv:1907.08124v2

ZADNIK Lenart     Inhomogeneous matrix product ansatz and exact steady states of boundary-driven spin chains at large dissipation.
I will present a site-dependent Lax formalism allowing for an exact solution of a dissipatively driven XYZ spin-1/2 chain in the limit of strong dissipation that polarizes the boundary spins in arbitrary directions. The constituent matrices of the ansatz for the steady state satisfy a simple linear recurrence that can be mapped into an inhomogeneous version of the quantum group Uq(sl2) relations.