New Angles on Integrability in Classical and Quantum Rule 54

• Rustem Sharipov (University of Ljubljana)

Room: Peterlin Pavilion The reversible cellular automaton Rule 54 (RCA 54) exhibits striking signatures of integrability, including stable solitons and ballistic transport. Nevertheless, a systematic structural formulation of its integrability has remained elusive. In this talk, I discuss a new perspective on integrability in classical RCA 54. I introduce a mechanism of "integrability by projection", whereby interacting solitonic dynamics with nontrivial phase shifts emerge from a projection of SWAP dynamics. From the quantum perspective, using recent remarkable work by Paletta and Prosen (arXiv:2603.25424), I will show that quantum Rule 54 is a limit of a integrable trotterization of the bond-transformed Heisenberg spin chain.

Correlation functions of the Lieb—Liniger model: long-time, large-distance asymptotics beyond thermal equilibrium

• Mikhail Minin (Bergische Universität Wuppertal)

Room: Peterlin Pavilion Dynamical two-point correlation functions are central objects in the study of quantum many-body systems. They encode the response to local perturbations, determine the transport coefficients, and in general provide the bridge between the microscopic quantum mechanical description and experimentally observable quantities. Obtaining their long-time, large-distance asymptotics for systems in thermal or non-thermal equilibrium, such as a generalised Gibbs ensemble, continues to be an open and difficult problem even for integrable models. We present rigorous results for the Lieb—Liniger model in the limit of infinite repulsion (also known as the impenetrable Bose gas and the Tonks—Girardeau gas), covering a large class of non-thermal equilibrium conditions and extending previous results established for the thermal equilibrium case. Starting with exact representations of correlation functions as Fredholm determinants of an integrable integral operator, which depends parametrically on distance $x$, time $t$, and on the filling fraction characterizing the thermal or non-thermal equilibrium conditions, we perform a rigorous asymptotic analysis using Riemann—Hilbert techniques. We identify two classes of filling fractions, characterized by the number of poles on the real axis (a generalization of Fermi points) that contribute, together with the unique saddle point, to the asymptotic expansion. For each class, we derive the asymptotic behaviour as a series in $x^{-1/2}$ as $x$ and $t$ go to infinity, for a fixed ratio $x / t$, with explicit closed-form expressions for the leading and sub-leading terms, logarithmic corrections, and overall constants. In the thermal equilibrium case, we verify our results by comparing them with the existing results in the literature and with numerical data, finding good agreement. Based on joint work with Frank Göhmann, Karol K. Kozlowski, and Alexander Weiße.

Observing quantum criticality at finite temperature through nonanalytic correlation times

• István Csépányi (Budapest University of Technology and Economics)

Room: Peterlin Pavilion Quantum phase transitions are characterized by non-analytic changes in ground-state properties as a control parameter is varied. At non-zero temperature, however, thermal fluctuations smooth out these singularities in static observables, making direct signatures of quantum criticality difficult to access experimentally. In this talk, I will show that dynamical properties can retain clear fingerprints of the underlying critical point even at finite temperature. Focusing on the Transverse-field Ising model as a paradigmatic example, we study the finite-temperature dynamics of the order parameter and demonstrate that its correlation time exhibits non-analytic behavior as the transverse field is tuned across the quantum critical point. In contrast to equilibrium expectation values, this dynamical quantity remains sharply sensitive to the underlying quantum phase transition and provides a direct probe of criticality in experimentally relevant finite-temperature regimes. I will discuss the scaling properties of this effect and its physical interpretation in terms of competing quantum and thermal fluctuations. As an outlook, these findings suggest that such non-analytic dynamical signatures may extend beyond the transverse-field Ising model, pointing toward a broader framework for detecting quantum criticality through finite-temperature correlation dynamics.

Coordinate Bethe Ansatz for the Thirring Quantum Cellular Automaton

• Saverio Rota (Università di Pavia)

Room: Peterlin Pavilion We explore the integrability of the 1+1-dimensional massless Thirring Quantum Cellular Automaton, which describes the discrete-time evolution of fermionic modes on a lattice with local, number-preserving interactions. The interaction serves as a discrete-time analogue of those found in integrable Hamiltonian systems such as the Thirring and Hubbard models. Using the coordinate Bethe ansatz, we analyse the spectrum of the unitary operator defining the QCA dynamics, constructing translationally invariant eigenstates as superpositions of plane waves related by permutations of particle spins and momenta. The discrete-time structure leads to distinctive features absent in continuous-time systems, in particular constraints arising from the periodicity of the quasi-energy spectrum, which induce degeneracies. We derive consistency relations among the amplitudes and show that they can be encoded in a two-body scattering matrix satisfying the Yang–Baxter equation. In the massless case, however, the dynamics renders this structure effectively trivial, reflecting strong kinematic constraints while preserving the characteristic form of the scattering matrix. These results provide the foundation for ongoing work on the massive case, where the insights gained here guide the construction of the Bethe ansatz and the treatment of the distinctive features of the QCA dynamics.

Integrability-breaking-induced Mpemba effect in spin chains

• Adam McRoberts (International Centre for Theoretical Physics)

Room: Peterlin Pavilion We show that there are two distinct mechanisms that can cause the symmetry-restoration Mpemba effect in spin chains with \textit{weakly broken} integrability, such that the asymptotic equilibration is diffusive, but the lifetime of anomalously fast spin hydrodynamics at low temperature is parametrically large. In particular, we consider isotropic spin chains quenched out of equilibrium by suppressing the -components, without inducing any net magnetisation. Initially, the restoration of isotropy is faster in hotter systems -- because they have more phase space available to scramble their initial conditions -- which may cause the equilibration curves to cross at early times in both integrable and non-integrable systems. At later times, however, the equilibration is effectively hydrodynamic, and the \textit{colder} systems start to equilibrate faster as the lifetime over which they evince superdiffusive spin hydrodynamics is parametrically larger -- but only in \textit{non}-integrable models. Depending on the details of the temperatures and the extent of the initial symmetry-breaking, two isotropy-restoration curves may have a crossing at early time, late time, neither, or both.

Leading UV Behaviour of Finite-Volume Vertex Operator Expectation Values in the Sine-Gordon Model from the Kink NLIE

• Apor Roth (Eötvös Loránd University)

Room: Peterlin Pavilion We study the ultraviolet (UV) limit of finite-volume expectation values of vertex operators in the sine-Gordon model using the kink nonlinear integral equation (NLIE) description of the conformal limit. By analysing the integrable formulation of vacuum expectation values, we conjecture an explicit analytic expression, given in terms of kink functions, for the leading asymptotic term in the small-volume expansion. This establishes a direct connection between the integrable finite-volume description and the expected conformal asymptotics. The proposed formula is tested against the analytic expression known from complex Liouville conformal field theory using high-precision numerics, showing agreement up to approximately 30 significant digits.

Linear response and exact hydrodynamic projections in Lindblad equations with decoupled Bogoliubov hierarchies

• Patrik Penc (University of Oxford)

Room: Peterlin Pavilion We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with non-Hermitian Hamiltonians. We use this formulation to obtain exact hydrodynamic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics.

Dynamical correlation functions from space-time duality

• Riccardo Travaglino (SISSA)

Room: Peterlin Pavilion While integrability is very powerful for the characterization of static properties of integrable systems, accessing the dynamics remains challenging and in general requires extra ingredients. In the talk I will describe the recently introduced framework of Space-Time duality (SD), which has allowed to finally characterize the evolution of Renyi entropies following quantum quenches (unifying integrable and chaotic quenches); further I will show how the framework can be extended to investigate the $n$-time cumulant generating function (or $n$-Full Counting Statistics, $n$-FCS) of extensive $U(1)$ charges in general integrable systems. I will explain how the fundamental ideas of SD allow to obtain the corresponding multi-time correlation functions in the ballistic regime, and to show that for quenches from some common choices of initial states these dynamical correlators trivialize in a remarkable way. Finally, I will comment about the insight that such structure gives on protocols in which the evolution of integrable systems is interspersed with projective charge measurements.

Quasiparticle picture for quench dynamics: non-pair structures, higher dimensions and symmetry-breaking

• Molly Gibbins (University of Nottingham)

Room: Peterlin Pavilion The problem of closed, many-body quantum dynamics is, in general, an exceedingly difficult one. On the one hand, the *entanglement entropy* became recognised around the turn of the century as a suitable proxy for the relaxation of local subsystems in the closed many-body setting. On the other, the densities of quasiparticles have since become widely used to characterise the dynamics of local observables in integrable systems at the coarse-grained level: the generalised hydrodynamic picture. In light of these points, a huge step forward was to realise that the correlations between these quasiparticles offer an effective description for the entanglement generated by a quantum quench. The resulting *quasiparticle picture* for entanglement growth has enjoyed remarkable success in a wide variety of settings, and has also been shown to be applicable to other measures of the Schmidt spectrum such as the negativity and entanglement asymmetry – and even beyond. In this talk I will outline the basic quasiparticle formulation of these measures and review some of its main extensions: crucial to this story will be the ‘generalised’ quasiparticle picture that we formalised in our first work [1], which accommodates both higher mode correlation structures and higher spatial dimensions. I will also touch on cases in which the picture breaks down, with emphasis on the discrete symmetry breaking considered in our second work [2]. [1] Gibbins, M. et al. Quench dynamics in lattices above one dimension: The free fermionic case. Phys. Rev. B 109, 224310 (2024) [2] Gibbins, M. et al. Translation symmetry restoration in integrable systems: The noninteracting case. Phys. Rev. B 112, L180307 (2025)

Determining Quantum Integrability Directly from the Hamiltonian

• Mizuki Yamaguchi (The University of Tokyo)

Room: Peterlin Pavilion Quantum integrability is usually characterized from two perspectives. One is **Yang-Baxter solvability**, formulated in terms of an R-matrix satisfying the Yang-Baxter equation, or a transfer matrix constructed from it. The other is conservation laws, formulated in terms of **infinitely many local conserved quantities** commuting with the Hamiltonian. From either viewpoint, however, it is generally difficult to decide whether a given Hamiltonian is integrable. In the Yang-Baxter framework, one usually starts by finding, often through nontrivial insight, a solution of a matrix-valued functional equation, and the Hamiltonian is then recovered as only part of the information encoded in it. Reversing this procedure, namely finding the corresponding R-matrix from a given Hamiltonian, is difficult in general. On the other hand, directly testing the existence of local conserved quantities requires solving large systems of linear equations, and is therefore impractical. Thus, determining integrability directly from the Hamiltonian remains a difficult problem. In this talk, I will report that, for isotropic nearest-neighbor spin chains, this problem admits an extremely efficient criterion [1,2]. More specifically, we consider Hamiltonians of the form $H=\sum_i\sum_{n=1}^{2S}J_n(S_i\cdot S_{i+1})^n$ for arbitrary S. We prove that, in this class, the condition known as the Reshetikhin condition is equivalent to integrability, both in the sense of Yang-Baxter solvability and in the sense of local conserved quantities. Namely, if the Reshetikhin condition holds, the system is Yang-Baxter solvable, the corresponding R-matrix can be constructed algorithmically, and infinitely many local conserved quantities can be generated. Conversely, if the Reshetikhin condition does not hold, the system is not Yang-Baxter solvable and has no nontrivial local conserved quantities. This result shows that, within the class of isotropic chains, integrable and non-integrable systems fall into two sharply distinct classes, and that the Reshetikhin condition provides a necessary and sufficient criterion distinguishing them. Finally, I will explain that some of the key lemmas used in the proof hold beyond the isotropic case. This suggests a new direction in the study of quantum integrable systems: to search the space of local Hamiltonians efficiently and exhaustively for integrable systems, and then solve them constructively. References [1] N. Shiraishi and M. Yamaguchi, Dichotomy theorem separating complete integrability and non-integrability of isotropic spin chains, Phys. Rev. B (2026). [2] N. Shiraishi, M. Yamaguchi, and F. Ishii, in preparation.

Bethe Ansatz with LLMs

• Istvan Vona (ELTE University, Wigner RCP)

Room: Peterlin Pavilion In recent months, Large Language Models and AI agents built on them were used successfully to solve research-grade problems in pure mathematics and theoretical physics. It is tempting to assume that this technology may be very successful in performing calculations in our field, integrability. As a first step, we investigated the capabilities of an LLM to work out the Bethe Ansatz equations for certain medium-range models [ https://arxiv.org/abs/2603.29932 ]. The talk is meant to be an invitation to share experiences, discuss best practices, and attitudes towards LLM results in our work.

Random Matrix Signatures of Classical Chaos

• Pavel Orlov (University of Ljubljana)

Room: Peterlin Pavilion Random matrix theory (RMT) is one of the main tools for studying quantum chaotic systems. Since quantum evolution is unitary, one can analyze the statistics of eigenvalues of the generators of unitary dynamics — for instance, energy-level statistics — and compare them with the corresponding RMT predictions. In this talk, I will argue that a similar approach can also be applied to classical systems, as classical observables likewise evolve unitarily. I will focus on discrete classical systems, for which the relevant RMT ensemble is given by random permutations. Concentrating on one-dimensional classical brickwall circuits and employing methods of space-time duality, I will demonstrate how RMT behavior emerges in discrete classical many-body systems.

Algebraic Bethe Ansatz for a multispecies extension of TASEP

• Christoph Obenaus (Instituto Superior Técnico)

Room: Peterlin Pavilion We consider a multispecies extension of the asymmetric simple exclusion process with hierarchical dynamics and species-dependent hopping parameters. On an integrable submanifold of parameter space, we construct an explicit Yang–Baxter formulation for the tilded Markov generator. The underlying local structure is governed by a coloured 0-Hecke-type algebra, which provides the natural setting for the Baxterization. Using the nested algebraic Bethe ansatz, we derive the general system of coupled Bethe equations for an arbitrary number of species. This is work in progress, in collaboration with Ali Zahra.

Topological defects in non-Hermitian lattice model

• Madhav Sinha (Rutgers University, New Brunswick)

Room: Peterlin Pavilion In this talk, I will construct topological defects in non-Hermitian lattice models using integrability. I will demonstrate defect RG flows between different defects and analyze them using the g-function. This work is done in collaboration with Ananda Roy, Hubert Saleur, and Thiago Silva Tavares.

Symmetry-resolved and Field-space entanglement out-of-equilibrium

• Léonce Dupays (King's College London)

Room: Peterlin Pavilion This talk describes recent advances on entanglement out-of-equilibrium. In the first part, I will focus on symmetry-resolved entanglement, which describes how entanglement is distributed among the symmetry sectors of a system. In this context, charged moments of the reduced density matrix provide a natural starting point. I will show how these quantities can be studied using Ballistic Fluctuation Theory [1], a framework that describes large-scale ballistic fluctuations of conserved charges and associated currents and, through the height-field formulation of twist fields, gives access to the asymptotic behaviour of their two-point correlation functions [2]. This approach provides a rigorous derivation of results previously obtained from the phenomenological quasiparticle picture of entanglement spreading after pair-producing quenches [3]. In the second part, I will turn to a different notion of bipartition, namely field-space entanglement. Rather than splitting a single system in real space, one may consider two coupled one-dimensional gapless systems and ask how entanglement develops between the two fields themselves. For systems described by Luttinger liquid theory, I will discuss the dynamics of logarithmic negativity and mutual information following coupling quenches, at zero and finite temperature [4]. In particular, we obtain exact analytical results for their large-time averages and are able to characterise the early-time growth of entanglement. This provides a framework to study both quantum entanglement and total correlations in out-of-equilibrium multi-field systems, with potential experimental relevance for coupled Bose–Einstein condensates [5]. [1] B. Doyon, J. Myers, Annales Henri Poincaré (2019) [2] G. Li, L. Dupays, P. Ruggiero, arXiv (2026) [3] P. Calabrese, J. Cardy, J. Stat. Mech. (2005) [4] L. Dupays, T. Murthado, B-H. Tiang, N. Ng, P. Ruggiero, to appear (2026) [5] V. Gritsev, A. Polkovnikov, E. Demler, Phys. Rev. B (2007)

Integrable Deformations and the Onset of Quantum Chaos

• Ysla França Adans (Institute of Theoretical Physics — IFT/UNESP - Brazil)

Room: Peterlin Pavilion In this work, we investigate how perturbations affect the statistical properties of an integrable model. Using integrable and quasi-integrable deformations generated via the Boost Operator, we numerically analyze indicators of integrability breaking, such as level spacing distributions and Krylov complexity, to characterize the onset of quantum chaos. We apply these methods to nearest-neighbour deformations of the XXZ model and show that these systems exhibit a range of distinct physical behaviors. In particular, we compare perturbatively integrable models with weakly integrability-breaking long-range spin chains.

Generalised Hydrodynamics of dark soliton gases

• Adrien Escoubet (Université de Lille)

Room: Peterlin Pavilion We study the defocusing nonlinear Schrödinger (dNLS) equation, an integrable nonlinear partial differential equation ubiquitous in physics. This equation with nonzero boundary conditions admits soliton solutions: stable localised oscillations that scatter elastically. In the limit of a large number of solitons with random amplitudes, velocities and positions, called soliton gas, it is more relevant to characterise the resulting field by thermodynamic quantities, such as the average values of some observables, or the correlation functions. The framework of Generalised Hydrodynamics (GHD) has allowed for the description of the many-body behaviour of classical and quantum particle integrable systems [1, 2], with remarkable agreement between the theory and the experiments [3]. The GHD for dNLS has already been built from the semi-classical limit of the Lieb-Liniger model, based on the radiative (non-solitonic) solutions of dNLS [4]. We derive a complementary GHD based on classical heuristic arguments, considering the solitons as point-like particles, which makes the statistical mechanics approach more natural and transparent. The exact procedure is similar to what has already been done for the Korteweg de Vries and Boussinesq equations [5, 6]. From an ansatz on the form of the partition function, we recover the soliton gas equivalent of the Yang-Yang equation, as well as expressions for the conserved charges and the two-point correlation functions in terms of the density of solitons. The soliton based formalism allows us to analytically solve the dressing equation for a particular class of soliton gases called dilute condensates, which we use to benchmark efficient numerical methods for the computations. [1] - Bertini, B., Collura, M., De Nardis, J., & Fagotti, M. (2016). Transport in Out-of-Equilibrium X X Z Chains : Exact Profiles of Charges and Currents. Physical Review Letters, 117(20), 207201. https://doi.org/10.1103/PhysRevLett.117.207201 [2] - Castro-Alvaredo, O. A., Doyon, B., & Yoshimura, T. (2016). Emergent Hydrodynamics in Integrable Quantum Systems Out of Equilibrium. Physical Review X, 6(4), 041065. https://doi.org/10.1103/PhysRevX.6.041065 [3] - Dubois, L., Thémèze, G., Dubail, J., & Bouchoule, I. (2026). Experimental investigation of a bipartite quench in a 1D Bose gas. SciPost Physics, 20(1), 008. https://doi.org/10.21468/SciPostPhys.20.1.008 [4] - Del Vecchio Del Vecchio, G., Bastianello, A., De Luca, A., & Mussardo, G. (2020). Exact out-of-equilibrium steady states in the semiclassical limit of the interacting Bose gas. SciPost Physics, 9(1), 002. https://doi.org/10.21468/SciPostPhys.9.1.002 [5] - Bonnemain, T., Doyon, B., & El, G. (2022). Generalized hydrodynamics of the KdV soliton gas. Journal of Physics A: Mathematical and Theoretical, 55(37), 374004. https://doi.org/10.1088/1751-8121/ac8253 [6] - Bonnemain, T., & Doyon, B. (2025). Soliton gas of the integrable Boussinesq equation and its generalised hydrodynamics. SciPost Physics, 18(2), 075. https://doi.org/10.21468/SciPostPhys.18.2.075

Generalized hydrodynamics of free fermions under extensive-charge monitoring

• Juan Pablo Bayona Pena (University of Bologna)

Room: Peterlin Pavilion We study transport dynamics of free fermions subject to the external monitoring of a conserved charge over an extensive region. Focusing on bipartition protocols, we consider monitoring the total particle number over half of the system, and study the profiles of local charges and currents at hydrodynamic scales. While the Lindbladian describing the averaged dynamics is non-local, we show that the profiles can be understood in terms of localized impurities. We present a general framework based on the generalized hydrodynamics (GHD) picture, allowing for a hybrid numerical-analytic solution of the quench dynamics at hydrodynamic scales. We illustrate our approach for domain-wall initial states, showing that monitoring leads to discontinuities in the profiles that become more pronounced as the rate increases and that lead to the absence of transport in the Zeno limit of infinite monitoring rates. Our GHD framework could be naturally extended to interacting systems, paving the way for a systematic study of transport of integrable models subject to extensive-charge measurements.

Exact quantum dynamics of interacting integrable models via Monte Carlo sampling

• Riccardo Senese (SISSA)

Room: Peterlin Pavilion Despite the exact solvability of the spectrum in interacting quantum integrable models, the computation of (dynamical) correlation functions remains a major open challenge analytically and numerically. A fundamental bottleneck is that the Lehmann representation for the correlators involves a summation over a number of form factors that scales exponentially with system size, rendering exact summations prohibitive for any classical computational resources. I will present recent progress based on Markov Chain Monte Carlo sampling of form factors and overlaps that enables the accurate reconstruction of correlation functions in (generalized) Gibbs ensembles [1], as well as out-of-equilibrium following global quantum quenches [2], for generic energy densities, particle densities, and interaction strengths. To demonstrate the efficacy of the approach I will focus on the transverse-field Ising chain and the repulsive Lieb-Liniger gas, where a few benchmarks are available. Finally, I will address the origin of the absence of a Monte Carlo “sign problem”, and discuss scenarios in which it persists. [1] R. Senese, F.H.L. Essler; https://doi.org/10.1103/8qtr-dm7g [2] R. Senese, F.H.L. Essler; in preparation

Universal efficiency boost in prethermal quantum heat engines at negative temperature

• Alberto Brollo (Technical University Munich)

Room: Peterlin Pavilion Quantum heat engines lie at the intersection of quantum thermodynamics and non-equilibrium many-body physics. Technological advances in quantum platforms have motivated studies beyond canonical equlibrium. In this talk, I will discuss whether prethermalization enhances or reduces engine efficiency by investigating Otto cycles in quantum systems with varying numbers of conserved quantities. Additional conservation laws reduce efficiency at positive temperatures, but enhance it in regimes of negative temperatures. Our findings stem from general thermodynamic inequalities for infinitesimal cycles, and we provide evidence for integrable models undergoing finite cycles using Generalized Hydrodynamics. The relevance of our results for quantum simulators is also discussed, providing an example of how theoretical advances in the theory of integrable systems can be used to design novel quantum devices. The talk is based on Nat. Commun. 16, 10593 (2025), joint work with Alvise Bastianello and Adolfo del Campo.

Relaxation and phase locking in tunnel-coupled 1D bosonic quasi-condensates

• Bence Fitos (Budapest University of Technology and Economics)

Room: Peterlin Pavilion We consider a prime example of simulating interacting relativistic QFT with cold atoms: the realisation of the sine-Gordon model by tunnel-coupled quasi-1D Bose gases. While experiments have shown that it can realise the sine-Gordon model in equilibrium, studies of non-equilibrium dynamics have revealed a phase-locking behaviour that stands in contrast to predictions from sine-Gordon field theory. Here, we examine a one-dimensional field-theoretic model of the system and find that the phase-locking behaviour can be understood in terms of the presence of the longitudinal harmonic trap, and that the additional degrees of freedom known to be present in the experiment do not appear to play a significant role. Therefore, the experimental setup provides a good simulator of the sine-Gordon quantum field theory, even out of equilibrium, if the inhomogeneous background induced by the trap is taken into account. Furthermore, our results support the idea that modifying the longitudinal trap to a box shape should result in agreement with standard sine-Gordon dynamics. The main remaining open issues are to account for 3D corrections and model the effect of the boundaries.