Invited talks (50 min)
Véronique Terras : T.B.A.
Lenart Zadnik : T.B.A.
Chiara Paletta: On the (hidden) integrability structure of the deformed rule-54 reversible cellular automaton.
I will discuss the integrability property of a stochastic and quantum deformation of the Rule 54 cellular automaton: the simplest microscopic (deterministic) reversible model in 1+1 discrete space and time dimensions with strong local interactions. First, I will introduce the Rule 54 model and its two deformations: (i) In the stochastic case, I couple the system to stochastic boundary reservoirs and show that the resulting non-equilibrium steady states can be constructed explicitly in matrix product form. (ii) In the quantum case, I explain how the model can be embedded into the Yang-Baxter integrability framework and provide an expression of the Lax operator, the operator responsible for the existence of an extensive number of conserved quantities that con- strain the dynamics. It turns out that Yang-Baxter integrability is more common than previously thought!
Based on 2603.25424 with T. Prosen.
Mitchio Jimbo: Affinization of shifted quantum toroidal gl2.
We give a realization A0 of quantum toroidal algebra associated to gl2 which can be viewed as an affinization of the Drinfeld new realization of quantum affine gl2. We use this realization to define an affinization AN of shifted quantum affine gl2 depending on an integer N. We construct a family of representations using intertwiners (analogues of primary fields). We also mention coproduct issues and the case of gln.
This is a joint work with B. Feigin and E. Mukhin.
Katja Klobas : Integrability of Floquet-PXP model at the deterministic point.
Rafael I. Nepomechie: Preparing Bethe states using Gray codes.
Preparing a given quantum state on a quantum computer using elementary unitary gates is an interesting but challenging problem. We focus here on the preparation of exact eigenstates of the spin-1/2 Heisenberg quantum spin chain, and of its integrable higher-spin and higher-rank generalizations. We consider an approach that makes use of a Gray code — a sequence of strings of integers, such that each string differs in a minimal way from its successor; introduced in the 1940’s for telecommunication, and much-studied in combinatorics.
Benjamin Doyon : T.B.A.
Standard talks (20 min)
Ysla F. Adans: Classifying Integrable Deformations in Quantum Spin Chains.
In this work, we investigate nearest-neighbour deformations of integrable models. In our previous paper, ’On deforming and breaking integrability’ (2603.17018), we established the framework to construct deformation terms that satisfy the commutation relations of conserved charges through an order-by-order expansion of the Hamiltonian using the Boost Operator method, applying this framework to the XXZ model. In this presentation, I will review these results, demonstrating that such deformations naturally fall into three distinct classes: those that break integrability, those that strictly preserve it, and those that remain integrable only perturbatively up to a given order. Finally, I will present the new results of our current work, which extends this formalism to the one-dimensional Hubbard model. We will discuss the physical and algebraic properties arising from this new application, highlighting the structure of the quasi-integrable deformations.
Sergei Adler : Fermionic basis in Conformal Field Theory: the free fermion point.
Riccarda Bonsignori: Entanglement Hamiltonian after a local quench.
Understanding the structure of entanglement in extended quantum systems is a fundamental problem in theoretical physics. In this framework, a central object is the so-called entangle- ment (or modular) Hamiltonian (EH), defined as the logarithm of the reduced density matrix, that encodes the full structure of bipartite entanglement. In general the EH is very hard to compute and is not even expected to be a local operator. However, in relativistic quantum field theory the locality of the modular Hamiltonian for half-space bipartitions is ensured by the Bisognano–Wichmann theorem, which expresses it as an integral of the energy density with a linear spatial weight. In the presence of conformal symmetry, this result can be extended to other geometries and to some non-equilibrium settings. Since the Bisognano–Wichmann theorem is for- mulated within relativistic quantum field theory, a natural question concerns its applicability to lattice many-body systems whose low-energy properties are described by a conformal field theory, but which explicitly break Lorentz invariance. Several results addressing this question exist in equilibrium situations, while a lattice realisation of the time-dependent EH in out-of-equilibrium dynamics is still missing.
In this talk, I will present the study of the dynamics of the EH in a system of one-dimensional free fermions, following a local joining quench of two initially disconnected half-chains in their ground states. Applying techniques of conformal field theory, a local expression of the EH is derived, where the left- and right-moving components of the energy density are associated with different weight functions. The results are then compared to numerical calculations for the hopping chain, which requires to consider a proper continuum limit of the lattice EH, obtaining a good agreement with the field-theory prediction.
Based on: R. Bonsignori and V. Eisler, JHEP 2026, 232 (2026).
Matthieu Cornillault : Modified rational six vertex model : new formula, homogenous and thermodynamic limits.
Mathieu Dabrowski : New integrable Markov processes from set-theoretical R-matrices.
Gwenaël Ferrando: Exact Three-Point Functions in N = 2 Superconformal Field Theories.
We propose an integrability approach for planar three-point functions at finite coupling in N = 2 superconformal field theories obtained as ZK orbifolds of N = 4 super Yang-Mills (SYM). Generalising the hexagon formalism for N = 4 SYM, we reproduce the structure constants of Coulomb branch operators, previously obtained by supersymmetric localisation, as exact functions of the ’t Hooft coupling. Our analysis explains the common physical origin of Fredholm kernels in integrability and localisation.
This talk is based on arXiv:2503.07295 written with S. Komatsu, G. Lefundes, and D. Serban.
Oleksandr Gamayun : Beyond universal exponents in one-dimensional quantum liquids.
Luttinger liquid theory offers a powerful framework for understanding one-dimensional quantum systems of bosons, fermions, and spins. A central prediction of this theory is the universal power-law behavior of correlation functions, with exponents determined by a single parameter tied to the system’s thermodynamics. While these universal features are well established, the precise, non-universal details require more refined tools. In this talk, I will explain how such details can be obtained from combinatorial methods based on the finite-size scaling of the matrix elements and how these techniques can be extended to capture subleading asymptotics and treat finite-temperature behavior. As concrete examples, I will focus on strongly interacting systems where correlation functions take an elegant form involving Fredholm determinants of generalized sine kernels.
Sascha Gehrmann: Exact Strong Zero modes in Integrable Systems.
Strong zero modes are operators that commute with the Hamiltonian up to corrections that are exponentially small in system size, leading to robust spectral degeneracies throughout the many-body spectrum. In this talk, I will introduce the notion of exact strong zero modes, discuss their key properties and physical implications, and present evidence that they are not exceptional objects but rather a generic feature of a broad class of integrable models.
Arthur Hutsalyuk : Full counting statistics in integrable models.
Full counting statistics (FCS) of operators is a central object of study in statistical physics. Using the quantum inverse scattering method and the modified algebraic Bethe ansatz, we derive an explicit expression for the FCS in the form of a form factor expansion. This expansion provides the basis for establishing the asymptotic behavior of the FCS. We further consider quantum quenches from integrable initial states and obtain the corresponding long-distance asymptotics.
The presentation is partially based on arXiv:2509.13928 by S. Belliard and A. Hutsalyuk.
Yuan Miao: Lattice non-invertible symmetry from non-commuting transfer matrices.
The spin-1/2 XXZ chain, or six-vertex model, is a prototypical quantum integrable model governed by the Yang–Baxter equation. At roots of unity, it admits non-Abelian quasi-local conserved charges generating a representation of the Onsager algebra. I will explain how this Onsager symmetry follows from the non-commuting transfer matrices of the τ2 model. The same construction yields lattice operators whose fusion rules realise the Tambara–Yamagami fusion category TY(ZN), providing a lattice counterpart of the non-invertible symmetries of the corresponding c = 1 compact boson CFT. I will conclude with implications for representation theory and quantum dynamics.
Anrdrii Liashyk: On the co-property of Bethe vectors.
In this talk, I want to clarify the importance of the co-property for Bethe vectors in periodic and open spin chains. Using this property, we prove several classical identities for partition functions and scalar products of vectors. We also answer some open questions in this field. I also want to present the ”attenuation” procedure, which allows us to obtain results for a periodic chain from an open one.
Maria Matushko : R-matrix Dunkl operators and spin Calogero--Moser system.
The Calogero-Moser model is a celebrated example of a completely integrable system, with numerous connections to several areas of mathematics and physics. It describes a system of $n$ of identical particles scattering on the line with inverse-square potential. There are also trigonometric, hyperbolic and elliptic version of this model. The integrability of the system can be shown in different ways, for example, constructing the higher Hamiltonans via Dunkl operators. We propose an R-matrix generalization of the quantum elliptic Calogero-Moser system, based on the Baxter--Belavin elliptic R-matrix. This is achieved by introducing R-matrix-valued Dunkl operators so that commuting quantum spin Hamiltonians can be obtained from symmetric combinations of those. Using the freezing procedure, we construct integrable long-range spin chains.
The talk is based on the joint work with Oleg Chalykh arXiv:2509.18989
Rob Klabbers: Twisted long-range chains.
I will discuss a deformation of the Haldane-Shastry (HS) spin chain obtained by an explicit twisting of the chain, found by Fukui and Kawakami, and whose solvability and underlying integrability are far from understood. I show how part of the spectrum can be recovered by an explicit comparison to the original HS chain. The case of maximal twisting is extremely special and occurs in many different forms throughout the literature. Its simplest identity is as the supersymmetric HS chain for which the fundamental excitations, i.e. its spinons, are free fermions. Moreover, this twisted family is the long-range limit of an elliptic family that generalises the elliptic Inozemtsev chain and connects to the twisted XXX model.
Mikhail Minin : Exact asymptotic analysis of the correlation functions of the Bose gas beyond thermal equilibrium.
Anastasiia Trofimova : One Kernel to Rule Them All: Universal Structure in the Bethe Ansatz for Stochastic Processes.
The large deviation functions of integrable stochastic processes --- ASEP, q-boson ZRP, asymmetric avalanche process, and their relatives --- are all governed by a single nonlinear integral equation with the same kernel. We explain why: the Uq(sl2) Lax operator fixes the kernel independently of the model, while model-specific data enters only through the quantum Wronskians $\phi^\pm$. The derivation passes through the TQ, TP, and PQ polynomial relations and makes the underlying particle-hole duality manifest.
Ana Retore: Dynamical Temperley-Lieb and the Zk Orbifold Hamiltonian.
The XXZ spin-chain Hamiltonian has a well-known realization in terms of Temperley-Lieb generators, providing a powerful algebraic framework for understanding its structure. Motivated by this connection, I will discuss the Zk orbifold Hamiltonian appearing in N = 2 superconformal field theory under a new perspective. Although this Hamiltonian is not integrable in the conventional sense, it shares several notable features with the XXZ model. In this talk I will show that its XZ sector admits a formulation in terms of dynamical Temperley-Lieb generators. I will also show a graphical representation of this construction.
Anahita Sarvi : Quasi-solitons of the 1D Bose gas at arbitrary interaction strength.
We build long-lived, localized excitations in a 1D Bose gas with contact repulsion (also known as the Lieb-Liniger model). Using a selective superposition of multi-hole momentum eigenstates, we demonstrate an enhancement of excitation lifetimes compared to previously proposed approaches. Venturing beyond the limits of the weak- and strong-interaction regimes, we numerically obtain soliton-like excitations at arbitrary interaction strength using ABACUS, building on our earlier analytical results in the infinite-repulsion (Tonks-Girardeau) regime. Our results showcase the significance of sustaining classical-like excitations in the finite-interaction regime, where the quantum nature of the system becomes inevitably prominent.
Pavel Orlov : Multiscale Analysis of the Eigenstate Thermalization Hypothesis in Integrable Systems.
The Eigenstate Thermalization Hypothesis (ETH) provides the standard framework for understanding thermalization in quantum chaotic many-body systems through the statistical properties of matrix elements of local observables. In contrast, the corresponding statistical description of matrix elements in integrable systems, where an extensive number of conserved charges strongly constrains the dynamics, remains far less understood. Developing such a description is essential for studying the mechanism of generalized thermalization in integrable models. In this work, we develop a multiscale framework for analyzing the statistics of off-diagonal matrix elements in integrable systems. Going beyond the conventional microcanonical ensemble, we introduce a scaling parameter that controls the magnitude of fluctuations of the conserved charges, thereby allowing us to systematically interpolate between finite microcanonical shells and ensembles with a much broader scale of fluctuations. We implement this program in a minimal integrable model that admits both efficient numerical calculations for system sizes well beyond the current state of the art and explicit analytical treatment. We show that the statistical distributions of off-diagonal matrix elements exhibit a rich dependence on the fluctuation scale, revealing how the hierarchy of conserved charges governs the structure of matrix elements. Our results provide a new perspective on the role of integrability in the statistics of matrix elements of local observables and establish a multiscale extension of the ETH paradigm for integrable quantum systems.
Friedrich Huebner: Hard rods generalized hydrodynamics without averaging.
Studying large scale dynamics of interacting many-particle systems is extremely demanding both analytical and numerical. Fortunately, there exist an effective asymptotic description, called hydrodynamics, based on averaging over local equilibrium states. Unfortunately, in general it is an open problem to understand its emergence, i.e. to connect the microscopic and the macroscopic description. This motivates to study the problem of hydrodynamic emergence in simple models with ex- act microscopic solutions, such as the integrable hard rods model (hard spheres in 1D). In arXiv:2408.04502, we had derived the diffusive-scale hydrodynamic equation. To our surprise the result was not of the expected Navier-Stokes type. To investigate this, we propose a radical strategy: to study the evolution of a single deterministic configuration, instead of a statistical ensemble of them. First, I will explain how one can meaningfully define hydrodynamics in this scenario. Then, I will use the new to show that diffusion is in fact absent in hard rods and that hydrodynamics even works for “unphysical” configurations very far from local equilibrium. In addition, the method also provides error bounds on the quality of the hydrodynamic approximation.
Based on arXiv:2507.17827.
Anup Anand Singh : Hitchin systems and the 3d mixed BF Lagrangian one-form.
In 1987, N. Hitchin introduced a construction that provides integrable models associated with the moduli space of stable holomorphic bundles over Riemann surfaces. This construction and its subsequent generalisations encompass a large class of integrable models referred to as Hitchin systems. In this talk, I will explain how to describe Hitchin systems variationally using the framework of Lagrangian multiforms. In the process, we are naturally led to a multiform action for 3d mixed holomorphic-topological BF theory with defects. Notably, this brings together for the first time the frameworks of Lagrangian multiforms and holomorphic-topological gauge theories, two recent major developments in Lagrangian methods for studying integrability. Finally, I will discuss the derivation of a simple 1d action which unifies several well-known integrable hierarchies, including those of rational and elliptic Gaudin models and a spin generalisation of the elliptic Calogero–Moser model.
This talk is based on joint work with V. Caudrelier, D. Harland, and B. Vicedo.