ALVES-PIMENTA Rodrigo :
Free fermionic and parafermionic quantum spin chains.
We will discuss a new family of quantum spin chains with multispin interactions whose spectrum has a free fermionic or parafermionic nature. Despite the free nature of the spectrum, these spin chains in general cannot be solved by the Jordan-Wigner transformation. However, exploiting integrability, it can be shown that the quasi-energies are related to the roots of certain characteristic polynomials given by higher-order recurrence relations. In particular, the so-called Laguerre bound for the largest root of the characteristic polynomial allows a very efficient computation of the mass gap, providing a relevant tool for the study of critical quantum chains with and without quenched disorder. Beyond the spectral level, many interesting aspects of the Hamiltonians remain to be understood, for example, the computation of correlation functions and entanglement entropy.
pdf file of the presentation
ATAI Farrokh :
E8 symmetry of the van Diejen model through gauge and integral transformations.
The quantum van Diejen model is an integrable many-body system defined by a family of mutually commuting analytic difference operators that is known to have hyperoctahedral symmetry in its variables and $E_8$ Weyl group symmetry in its parameters (under certain constraint).
In this talk, I present how the $E_8$ symmetry can be realized explicitly in terms of gauge and integral transformations using Ruijsenaars' elliptic Gamma function and how these transformations allow us to construct explicit eigenfunctions of the van Diejen model, under certain constraints on the model parameters. In particular, the transformations also yield eigenfunctions given by $BC$-type elliptic hypergeometric integrals.
The talk is based on joint work (arXiv:2203.00498) with M. Noumi.
pdf file of the presentation
BELLIARD Samuel :
Modified Algebraic Bethe Ansatz.
I will discuss a way to calculate spectrum and states for models without U(1) symmetries such as the open XXZ spin chain. The modified algebraic Bethe ansatz will be described in that case, and off-shell action of the related transfer matrix will be established. It will allows to calculate Slavnov's formula for scalar product of the associated states.
pdf file of the presentation
BOCINI Saverio :
On the hydrodynamical description of connected correlations.
Generalized hydrodynamics (GHD) has been successfully applied to compute the expectation value of local observables in integrable systems prepared in several inhomogeneous set-ups, among which the archetypical examples are partitioning protocols. However, GHD relies on the assumption of locality and, when applied to correlations, this powerful description shows its limitations: a correlation is characterised by multiple lengths and it is not evident in which limits a generalised hydrodynamic theory can be effective. The corrections to the GHD’s asymptotic values come both from higher-order GHD and from independent contributions that can not be incorporated in the theory. In this talk, I will address the problem of the typical size of the ``cells in space'' at the Euler scale in which correlations can be described by generalised hydrodynamic
pdf file of the presentation
BONSIGNORI Riccarda :
Dynamics of symmetry-resolved entanglement measures in free fermionic systems.
The presence of a global internal symmetry in a quantum many-body system is reflected in the fact that the entanglement between its subparts is endowed with an internal structure, namely it can be decomposed as sum of contributions associated to each symmetry sector. The study of the symmetry resolution of entanglement measures provides a formidable tool to probe the out-of-equilibrium dynamics of quantum systems. In this talk I will present the results of a series of works, done in collaboration with Gilles Parez and under the supervision of Prof. Pasquale Calabrese, devoted to the study of the dynamics of three different symmetry-resolved entanglement measures after a global quantum quench, namely the symmetry-resolved entanglement entropy, mutual information and negativity. In the context of free fermions, we are able to provide analytical results for the relevant time-dependent quantities. Moreover, we argue that our results can be understood in the framework of the quasiparticle picture for the entanglement dynamics, and provide a conjecture that we expect to be valid for generic integrable models.
pdf file of the presentation
CAETANO João :
Crosscap states in integrable models.
In this talk, I will describe crosscap states in integrable field theories and spin chains in 1+1 dimensions. I will derive an exact formula for overlaps between the crosscap state and any excited state in integrable field theories with diagonal scattering. I will then compute the crosscap entropy, i.e. the overlap for the ground state, in some examples. In the examples analyzed, the result turns out to decrease monotonically along the renormalization group flow except in cases where the discrete symmetry is spontaneously broken in the infrared. I will discuss crosscap states in integrable spin chains, and obtain determinant expressions for the overlaps with energy eigenstates. I will comment on the realization of crosscap states in holography.
pdf file of the presentation
FAULMANN Saskia :
Absence of string excitations in the low-T spectrum of the quantum transfer matrix of the XXZ chain.
The eigenvalues of the quantum transfer matrix (QTM) of the XXZ spin-1/2 chain in the Trotter limit are parameterized by solutions of non-linear integral equations (NLIEs). We analyze these equations in the low-temperature limit for the model in the antiferromagnetic massless regime for $0<\Delta<1$ at finite magnetic field $h>0$. To leading order in $T$ the solutions of the NLIEs are determined by the dressed energy, which, in turns, is the solution of a linear Fredholm integral equation of the second kind. A rigorous characterization of the properties of the dressed energy in different regions of the complex plane, in conjuction with a thorough study of the subsidiary conditions that determine the excitation parameters in the solutions of the NLIEs, allows us to show that the excited states of the QTM are all of particle-hole type and that there are no string excitation in the low-$T$ limit, as long as the magnetic field is kept finite.
pdf file of the presentation
FRAHM Holger :
Density matrices for RSOS models.
Local operators in interaction round a face models can be expressed in
terms of generalized transfer matrices. Using the properties of the
local Boltzmann weights we derive discrete functional equations
satisfied by the reduced density matrices for a sequence of
consecutive sites in inhomogeneous generalizations of these models.
For the restricted solid-on-solid (RSOS) models we find that these
density matrices can be 'factorized', i.e. expressed in terms of
nearest-neighbour correlators with coefficients which are independent
of the model parameters. Determining these coefficients we obtain
explicit expressions for multi-point local height probabilities.
pdf file of the presentation
GAMAYUN Oleksandr :
Effective form factors for free fermionic models at finite temperature.
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 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 the asymptotic behavior of 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" resummations, we develop a phenomenological approach that introduces the effective form factors and reduces the problem to the zero temperature case. The information about the initial state is transferred into the scattering phase of the effective fermions.
I will demonstrate how this works for correlation functions in the XY model, mobile impurity, and the sine-kernel Fredholm determinants.
pdf file of the presentation
GÖHMANN Frank :
Thermal form factor expansions for the dynamical two-point functions of local operators in integrable quantum chains.
Evaluating a lattice path integral in terms of spectral data and matrix elements
of a suitably defined quantum transfer matrix, we derive form factor series
expansions for the dynamical two-point functions of arbitrary local operators
in fundamental Yang-Baxter integrable lattice models at finite temperature.
The summands in the series are parametrized by solutions of the Bethe Ansatz
equations associated with the eigenvalue problem of the quantum transfer
matrix. We elaborate on the example of the XXZ chain for which the solutions
of the Bethe Ansatz equations are sufficiently well understood in certain
limiting cases. We work out in detail the case of spin-zero operators in the
antiferromagnetic massive regime at zero temperature. In this case the thermal
form factor series turn into series of multiple integrals with fully explicit
integrands. These integrands factorise into an operator-dependend part,
conjectured to be determined by the so-called Fermionic basis, and a part which
we call the universal weight as it is the same for all spin-zero operators. The universal
weight can be inferred from our previous work. The operator-dependent part
ist rather simple for the most interesting short-range operators. It is determined
by two functions ρ and ω for which we obtain explicit epxressions in the
considered case. As an application we rederive our explicit form factor series
for the two-point function of the magnetization operator and obtain analogous
expressions for the magnetic current that allow us to compute the optical
conductivity of the model.
pdf file of the presentation
HUTSALYUK Arthur :
Loschmidt echo in unitary circuits via the polynomial ring theory.
We consider a method of computation of correlation functions and relaxation processes (such as Loschmidt echo) in integrable spin chains and unitary circuits using form factor summation method combined with a polynomial ring theory. In cases when Bethe equations can expressed in terms of rational functions only, it is possible to simulate the behaviour of the systems using the fact that observables are the rational functions of spectral parameters, if it is possible to describe the system using relatively small number of particles.
pdf file of the presentation
ISHIGURO Yuki :
Bethe string solutions for the non-Hermitian spin chain.
To extend the analytical method of the Bethe ansatz such as the TBA for non-Hermitian systems, we investigate string solutions for the ASEP. The ASEP can be regarded as an extension of the XXX model by a single parameter that represents non-hermicity. We will show the formalism of string solutions for the ASEP, and explain how string solutions for the XXX model are deformed by non-hermicity.
pdf file of the presentation
KITANINE Nikolai :
Form factors and complex Bethe roots.
The asymptotic computation of the Slavnov determinant in the thermodynamic limit is an extremely important problem for the analytic study of the correlation functions and for factors of quantum integrable systems. In this talk I 'll describe a method to compute the Slavnov determinant in the thermodynamic limit in the case of spin chains with zero external magnetic field. As an illustration I'll show how to compute analytically form factors of the XXX spin chain for the low lying excited states. I'll also explain how to deal with the the complex Bethe roots.
pdf file of the presentation
KOCH Rebekka :
Bound state production in the 1d Bose gas.
Out-of-equilibrium phases of matter have triggered a lot of attention in the last decade, since new and interesting physical phenomena with no equilibrium counter parts can arise. The 1d interacting Bose-gas for example possesses bound states for attractive interactions but is experimentally highly unstable at equilibrium. However, these bound states become stable out-of-equilibrium since the 1d Bose-gas is integrable and thus, thermalization is absent.
Strongly interacting systems are notoriously hard to tackle, but due to integrability we can analytically investigate slow interaction changes from the repulsive to the attractive regime using the framework of Generalized Hydrodynamics (GHD). We obtain exact predictions for the bound state production and completely characterize the non-equilibrium state.
pdf file of the presentation
LACROIX Sylvain :
Integrable sigma-models at RG fixed points: quantisation as affine Gaudin models.
In this talk, I will present first steps towards the quantisation of integrable sigma-models using the formalism of affine Gaudin models, approaching these theories through their conformal limits. The talk will mostly focus on a specific example called the Klimčík (or bi-Yang-Baxter) model. After recalling the relation between this theory and affine Gaudin models at the classical level, I will explain how its integrable structure splits into two decoupled chiral parts in the conformal limit, built respectively from left-moving and right-moving degrees of freedom. Finally, I will briefly sketch how the quantisation of these chiral integrable structures can be studied using the language of affine Gaudin models and vertex operator algebras. This is based on joint work with G. Kotousov and J. Teschner.
pdf file of the presentation
LAMERS Jules :
New results for the q-deformed Haldane--Shastry spin chain.
The Haldane--Shastry model is an isotropic long-range spin chain with many interesting properties; amongst others it enjoys Yangian symmetry and has wave functions with explicit expressions in terms of Jack polynomials. These properties can be understood from a connection to the trigonometric quantum Calogero--Sutherland model and Dunkl operators, which provide the model's underlying quantum-integrable structure.
In my talk I will discuss the XXZ-like generalisation of the Haldane--Shastry spin chain. I will introduce the model, point out its similarity to the inhomogeneous XXZ spin chain, and outline its key properties. In addition I will present preliminary findings for the free-fermion point q=i.
Based on joint work with D. Serban and V. Pasquier, unpublished results, and ongoing work with D. Serban and A. Toufik.
pdf file of the presentation
LEVKOVICH-MASLYUK Fedor :
Separation of variables and correlation functions.
I will present new results in the separation of variables (SoV) program for integrable models. The SoV methods are expected to be very powerful but until recently have been barely developed beyond the simplest gl(2) models. I will describe how to realize the SoV for any gl(N) spin chain and demonstrate how to solve the longstanding problem of deriving the scalar product measure in SoV. In particular, I will present a completely explicit expression for the measure. Using these results I will show how to compute a large class of correlation functions and overlaps in a compact determinant form. I will also present applications of SoV in 4d integrable CFT's such as the fishnet theory where it allows one to compute exactly a set of nontrivial observables.
pdf file of the presentation
LIASHYK Andrii :
Bethe vectors of models with non-difference R-matrices.
In recent years, we have explored the construction of Bethe Vectors which is based on the projective formula of Drinfeld currents.
It was discovered for describing the off shell Bethe vectors of model with symmetry of type A series and describes well the important properties of the Bethe vectors.
This construction also showed itself well for describing systems with other types of symmetries, for example BCD.
In this talk, I want to present some results about how this formula works for model with non difference R-matrices, like Nazarov (quiver super Lie algebras) and Bariev.
pdf file of the presentation
MAILLET Jean-Michel :
On algebraic and geometric structures of integrable models.
pdf file of the presentation
MATUSHKO Maria :
Anisotropic spin generalization of elliptic Macdonald-Ruijsenaars operators and R-matrix identities.
We propose commuting set of matrix-valued difference operators in terms
of the elliptic Baxter-Belavin R-matrix in the fundamental representation of
gl_M. In the scalar case M=1 these operators are the elliptic Macdonald-Ruijsenaars operators, while in the general case they can be viewed as anisotropic versions of the quantum spin Ruijsenaars Hamiltonians.
In scalar case Ruijsenaars proved that commutativity of the operators written in the form with arbitrary function is equivalent to the system of functional equations and the elliptic Kronecker function solves this system.
We show that commutativity of the operators for any M is equivalent to a set of R-matrix identities. The proof of identities is based on the properties of elliptic R-matrix including the quantum and the associative Yang-Baxter equations. As an application of our results, we introduce elliptic generalization of
q-deformed Haldane-Shastry model.
pdf file of the presentation
McCOY Barry :
Ising Correlations: open questions.
The correlation functions C(M,N) on the anisotropic square lattice are only very well understood for the diagonal case M = N where they are given by an N × N Toeplitz determinant and are tau functions of a Painlevé VI equation. In this talk I will present recent progress on extending these results to the case of C(M,N) with M≠ N.
pdf file of the presentation
MEDENJAK Marko :
Distinguishing between quantum many-body integrability and chaos: Insights from quantum cellular automata
.
Classical integrable systems are fundamentally different from their chaotic counterparts as the close-by trajectories do not separate exponentially fast but remain close-by, which makes their dynamics much more tractable and less complex. In the talk I will make an overview of different proposals to distinguish between the quantum integrable and chaotic local many-body dynamics from the point of view of complexity, and present results about it obtained from explicit solutions of the dynamics in interacting super-integrable cellular automata.
pdf file of the presentation
MENEGHELLI Carlo :
Pre-fundamental representations for the Hubbard model and AdS/CFT.
There is a class of representations of quantum groups, referred to as prefundamental representations, that plays an important role in the solution of integrable models. The first example of such representations was given by V. Bazhanov, S. Lukyanov and A. Zamolodchikov in the context of two dimensional conformal field theory in order to construct Baxter Q-operators as transfer matrices. At the same time, there is a rather exceptional quantum group that governs the integrable structure of the one dimensional Hubbard model and plays a fundamental role in the AdS/CFT correspondence. In this talk I will introduce prefundamental representations for this quantum group, explain their basic properties and discuss some of their applications.
pdf file of the presentation
MORIN-DUCHESNE Alexi :
Universality and conformal invariance in critical percolation models.
In this talk, I will describe our investigations of the universal behaviour of two critical percolation models: site percolation on the triangular lattice and bond percolation on the square lattice. Both are Yang-Baxter integrable models that can in principle be solved exactly. In the scaling limit, they are conformally invariant and described by non-unitary representations of the Virasoro algebra. I will describe our calculation of the models' partition functions on the cylinder and torus. This is joint work with A. Klümper and P.A. Pearce.
pdf file of the presentation
NEPOMECHIE Rafael :
Bethe ansatz and quantum computing.
We begin with a brief review of the Heisenberg quantum spin chain and its remarkable solution found by Bethe. We then review a probabilistic algorithm for preparing exact eigenstates of this model on a quantum computer. An exact formula for the success probability is presented, and the computation of correlation functions is discussed. A generalization of the algorithm to open chains with boundaries is also noted.
pdf file of the presentation
OSHIMA Kazuyuki :
Elliptic quantum toroidal algebras and their representations.
In this talk, we define an elliptic analogue of quantum toroidal algebras associated with simple Lie algebras.
We then introduce Z algebra structure of the elliptic quantum toroidal algebras. Also we show that several representations for quantum toroidal algebras can be extended to the elliptic case.
This is a joint work with Hitoshi Konno (Tokyo University of Marine Science and Technology).
pdf file of the presentation
PAKULIAK Stanislav :
Recent advances in algebraic Bethe ansatz.
Equivalence of two realizations of quantum loop algebras associated to all series of
non-exceptional affine Lie algebras is reviewed. New results for the twisted quantum
loop algebras are presented. Central elements in R-matrix formulation of
the quantum loop algebras can be used to determine algebraically independent
generating series for these algebras in terms of Gaussian coordinates of
fundamental L-operators. Embedding theorem of the smaller algebra in the
bigger one is formulated and allows to find commutation relations between
Gaussian coordinates and the generating series in 'new' realisation of the quantum
loop algebras.
pdf file of the presentation
PRIMI Nicolo :
Form factors for sl(N) spin chains via Separation of Variables.
In integrable quasi-periodic spin chains with sl(N) symmetry, Functional Separation of Variables allows to compute scalar products between any so-called factorisable state, which includes all eigenvectors of the tower of conserved charges, in a compact determinant form. In this talk, we introduce Principal Operators, which are a special family of operators that generate the full Yangian algebra Y_n and give access to all observables. Using the new technique of Character Projection, we show that off-diagonal form factors of the Principal Operators on factorisable states can also be expressed as determinants. Furthermore, we show how to access form factors of anti-symmetrised multiple insertions of principal operators via the same techniques. Finally, we explicitly obtain matrix elements of the same principal operators on the so-called SoV basis. These can be used to obtain form factors on factorisable states of any number of insertions of principal operators, opening the road to the computation of correlators of local operators.
pdf file of the presentation
ROSSI Marco :
On the origin of the correspondance between integrable models and differential equations.
We start from some functional relations as definition of a quantum integrable theory and derive from them a linear integral equation. This is extended, by introducing dynamical variables, to become an equation with the form of the Marchenko one. Then, we naturally derive from the latter a classical Lax pair problem. We exemplify our method by focusing on the massive version of the ODE/IM (Ordinary Differential Equations/Integrable Models) correspondence involving the classical sinh-Gordon (ShG) equation with many moduli/masses, as describing super-symmetric gauge theories and the $AdS_3$ strong coupling of scattering amplitudes/Wilson loops. Yet, we present it in a way which reveals its generality of application.
The talk is based on arXiv paper : 2106.07600 [hep-th] with D. Fioravanti and 2004.10722 [hep-th] (on JHEP) with D. Fioravanti and H. Shu
pdf file of the presentation
TERRAS Véronique :
On correlation functions of the XXZ open spin chain with unparallel boundary fieldss.
We consider the problem of computing the zero-temperature correlation functions of the open XXZ spin 1/2 chain for unparallel, non-longitudinal boundary magnetic fields. The complete spectrum and eigenstates of the model can be constructed by means of the quantum Separation of Variables. When a particular constraint is applied on the 6 boundary parameters, part of the spectrum can be characterized in terms of solutions of a homogeneous TQ-equation, i.e. in terms of usual Bethe equations, with corresponding eigenstates coinciding with generalized Bethe states. We explain how to generically compute the action of a basis of local operators on such kind of states, and this under the most general boundary condition on the last site of the chain. As a result, we can compute the matrix elements of a set of local operators in any eigenstate described by the homogenous T Q-equation. Assuming, following a conjecture of Nepomechie and Ravanini, that the ground state itself can be described in this framework, we obtain multiple integral representations for these matrix elements in the half-infinite chain limit.
pdf file of the presentation
TROFIMOVA Anastasiia :
Crossover scaling functions in the asymmetric avalanche
process.
I would like to talk about the particle current in the asymmetric avalanche process on a ring. It is known to exhibit a transition from the intermittent to continuous flow at the critical density of particles. I present the exact expressions for the first two scaled cumulants of the particle current and explain how they were obtained in the large time limit $t\to\infty$ via the Bethe ansatz and a perturbative solution of the TQ-equation. The asymptotic analysis of these exact formulae shows that the scaled second cumulant per site, i.e. the diffusion coefficient or the scaled variance of the associated interface height, has the $O(N^{-1/2})$ decay expected for models in the Kardar-Parisi-Zhang universality class below the critical density, while it is growing as $O(N^{3/2})$ and exponentially times power law prefactor at the critical point and above. Also, I identify the crossover regime and obtain the scaling functions for the uniform asymptotics unifying the three regimes. We compare these functions to the scaling functions describing crossover of the cumulants of the avalanche size, obtained as statistics of the first return area under the time space trajectory of the Vasicek random process.
The talk is based on our work with Alexander Povolotsky, J. Phys. A: Math. Theor. 55 025202, arXiv: 2109.06318.
pdf file of the presentation
VILKOVISKIY Ilya :
Integrable structures of the affine Yangian, UV symmetries of integrable field theories.
In this talk I will report the recent progress in the study of integrable structures of the conformal field theories by the methods of the hidden affine Yangian symmetry. I will provide the standard Bethe ansatz picture, including local integrals of motion, Bethe vectors and Bethe equations. It turns out that the Integrals of Motion of the W algebras of type A coincide with the ones associated to an affine Yangian "spin chain" with periodic boundary conditions. The integrable structures of W algebras of types BCD are identified with affine Yangian "spin chains" with boundaries. The derivation of Bethe equations require additional techniques which were developed in series of papers arxiv: 2007.00535 2105.04018 , 2003.04234 .
pdf file of the presentation
ZADNIK Lenart :
Semilocal Gibbs ensembles and nonequilibrium symmetry-protected topological order.
I will revisit the problem of nonequilibrium time evolution in 1D quantum systems after a global quench. Global symmetries such as the spin flip symmetry in spin-1/2 chains can invalidate the standard picture of local relaxation to a (generalized) Gibbs ensemble. This occurs in models whose Hamiltonians possess conservation laws that are not local but act as such in the symmetry-restricted space where time evolution occurs. Their effective locality is possible due to the occurence of a hidden symmetry breaking, which is related to the emergence of a symmetry-protected topological order. I will discuss the ''semilocal (generalized) Gibbs ensembles'' that describe the stationary states emerging after infinite time in such models. Their exceptional features include logarithmic scaling of the excess entropy of a spin block, triggered by a local perturbation in the initial state, and meltdown of the order, induced either by a weak symmetry breaking or by an increase of the temperature.
pdf file of the presentation
KOZOLWSKI Karol :
Laudacio to Nikita Slavnov.
pdf file of the presentation
BOAT TRIP :
Les Bateaux Lyonnais.
At 18h00, 2 quai des Célestins, Lyon 2eme
web site
BANQUET :
La Mère Léa.
At 19h00, 11 quai des Célestins, Lyon 2eme
web site