Integrability and Nonequilibrium Phenomena in Spacetime-Modulated Systems

25 May 2026, 09:00 → 27 May 2026, 19:30 Asia/Tokyo

Kavli IPMU

Many physical systems of current interest operate far from equilibrium, where external driving, time-dependent interactions, and spatial modulation lead to rich and sometimes unexpected behavior. Examples range from periodically driven (Floquet) quantum systems to classical and quantum field theories with time-dependent couplings. Understanding such systems is a major challenge across condensed matter physics, statistical physics, high-energy theory and cosmology.

 

This workshop aims to bring together researchers studying nonequilibrium dynamics from complementary perspectives, with a particular focus on systems that retain special mathematical structures known as integrability. These structures allow exact or highly controlled descriptions of dynamics, even far from equilibrium, and have recently been identified in a growing number of time- and spacetime-modulated models both in high energy and condensed matter physics.

 

Topics will include driven and integrable systems with spatially modulated couplings, Floquet systems, relaxation and transport in nonequilibrium settings, and the use of integrability-based methods to analyze dynamical phenomena. Special emphasis will be placed on connecting recent developments on time-dependent integrable quantum mechanical models relevant to condensed matter physics with time-dependent integrable sigma models studied in high-energy physics.

 

By creating a common forum for researchers from different communities, the workshop seeks to encourage dialogue, clarify shared concepts, and highlight unifying principles underlying nonequilibrium behavior in spacetime-modulated systems. The program will emphasize interaction and discussion, with the goal of inspiring new collaborations and future research directions.

 

Invited Speakers:

Lewis Cole (University of Edinburgh)

Hiromi Ebisu (iTHEMS, RIKEN)

Ryusuke Hamazaki (iTHEMS, RIKEN)

Chisa Hotta (University of Tokyo)
Hosho Katsura (University of Tokyo)
Kohei Kawabata (ISSP, University of Tokyo)
Nat Levine (University of Amsterdam)
Chihiro Matsui (University of Tokyo)
Takashi Oka (ISSP, University of Tokyo)
Parameshwar Pasnoori (University of Maryland)
Junichi Sakamoto (University of Osaka)
Fumika Suzuki (University of Tokyo)
Anders Wallberg (École Polytechnique Fédérale de Lausanne)
Xueda Wen (Georgia Institute of Technology)
Takato Yoshimura (King’s College London)

 

Organizers:

Shota Komatsu (CERN)

Jiaxin Qiao (Kavli IPMU)

Masahito Yamazaki (Kavli IPMU & School of Science, University of Tokyo)

 

Monday 25 May

09:00 → 09:10 Safety briefing at Kavli IPMU

Speaker: Prof. Saeko Hayashi (Kavli IPMU)

09:10 → 10:10 Generalizing the Bethe ansatz

Quantum integrability is rooted in Bethe ansatz, which is a powerful mathematical framework that has been very successful in obtaining exact solutions to many-body Hamiltonians. Bethe ansatz in both the coordinate and algebraic incarnations is only applicable to Hamiltonians with constant coupling strengths. In this talk I will introduce the recently developed generalized Bethe ansatz framework, an exact method for solving a broad class of strongly interacting models with time-dependent coupling strengths that are based on quantum Yang-Baxter algebra. In this framework, the problem of solving the time-dependent Schrodinger equation can be reduced to a set of matrix difference equations, namely quantum Knizhnik-Zamolodchikov (qKZ) equations. The consistency of the solution gives rise to a set of constraint conditions on the time-dependent coupling strengths. For coupling strengths satisfying these conditions, the system is integrable, and the solution to the qKZ equations provides the explicit form of the exact wavefunction. I will further demonstrate that the conditions imposed by integrability are exactly equivalent to the renormalization-group flow equations of the corresponding Hamiltonian with time-independent coupling strengths, when the physical time of the driven system is identified with the logarithmic cutoff scale of the static problem t = log Λ, thereby revealing a deep connection between time-dependent integrability and the renormalization group flow. I will demonstrate how this formalism yields closed-form, non-perturbative solutions to paradigmatic models based on quantum Yang-Baxter algebra such as the Kondo model, the SU(2) Gross-Neveu model etc., whose interaction strengths vary in time. If time permits, I will conclude by discussing how this method can be applied to analyze novel dynamical phases that arise in driven quantum systems.

Speaker: Parameshwar Pasnoori (University of Maryland)

10:10 → 10:30 Tea break

10:30 → 11:30 Spatial modulation to reach the thermodynamic limit

We provide perspectives on spatial deformation techniques that are useful for driving local states to the equilibrium that mimics the thermodynamic limit.

The first case we focus on is the construction of boundary operators that effectively represent semi-infinite environments connected to the main finite system[1}. With this setup, the entanglement entropy measured in the central subsystem follows the conformal field theory (CFT) predictions not only for translationally invariant one-dimensional models but also for systems with quenched randomness. Furthermore, quench dynamics performed in this setup enable the tracking of long-time evolution while largely avoiding quasiparticle reflections from the boundaries.

Another example is the sine-square deformation (SSD), in which the local energy scale of the Hamiltonian is continuously reduced toward the system edges. This spatial modulation efficiently renormalizes the energy spectrum by compressing states into the low-energy sector and thereby strongly suppressing finite-size effects. While our earlier study [2] mainly focused on ground-state properties, we also found that SSD can yield physically meaningful finite-temperature behavior[3].

We also briefly mention our recent findings on the strongly correlated systems, where placing the spatially modulated on-site potentials yields the site-dependent excitation spectrum, each realizing the bulk ones for the corresponding chemical potential levels [4].

[1] S. Shimozono and C. Hotta, PRB, doi: 10.1103/bbnt-brjz
[2] C. Hotta, N. Shibata, PRB 86, 041108 (2012); C. Hotta, S. Nishimoto, N. Shibata, PRB 87, 115128 (2013).
[3] C. Hotta, T. Nakamaniwa, T. Nakamura, PRE 104,034133 (2021)
[4] K Matsuki, C Hotta, K Asano, PRB 112, 045146.

Speaker: Chisa Hotta (University of Tokyo)

11:30 → 13:00 Lunch break

13:00 → 14:00 Boundary scars

The eigenstate thermalization hypothesis (ETH) provides a theoretical framework for understanding how isolated quantum many-body systems reach thermal equilibrium. Recent experimental and theoretical studies have shown, however, that certain non-integrable systems can host atypical eigenstates that evade thermalization. These special states are called quantum many-body scars (QMBS), offering concrete examples of strong ETH violation.

In this talk, I will first give a pedagogical review of the algebraic methods used to construct such scar states. While obtaining exact eigenstates is usually restricted to integrable models, I will show how a tower of QMBS can be built in non-integrable systems by the repeated action of some judiciously chosen operator on a simple parent state.

I will then present our recent results based on integrability techniques such as integrable boundary states. These techniques allow us to construct a variety of models hosting exact QMBS in both one and higher dimensions. Time permitting, I will briefly touch on how crosscap states can be used to construct exact volume-law entangled eigenstates in non-integrable models.

[1] Kazuyuki Sanada, Yuan Miao, and Hosho Katsura, Phys. Rev. B 108, 155102 (2023).
[2] Kazuyuki Sanada, Yuan Miao, Hosho Katsura, arXiv:2411.01270.

Speaker: Hosho Katsura (University of Tokyo)

14:00 → 15:00 Scar subspaces stabilized by algebraic closure: Beyond equally-spaced spectra and exact solvability

We construct a class of quantum many-body systems hosting an su(3)-invariant scar subspace, extending the conventional paradigm of quantum many-body scars beyond equally spaced spectra and single-directional tower structures. Our construction is based on local constraints that realize algebraic closure within the scar subspace.
As a result, the spectrum in the subspace forms a multidirectional lattice structure parametrized by multiple independent quantum numbers, leading to qualitatively new dynamical signatures.

Importantly, the stability of the scar subspace does not rely on exact solvability of individual eigenstates. We show that algebraic closure preserves the invariant subspace even under perturbations that render the eigenstates analytically intractable, thereby realizing quantum many-body scars on an unsolvable reference state.
Our results identify algebraic closure as a unifying mechanism underlying scar subspaces beyond the conventional su(2) paradigm, and suggest a broader route toward nonthermal dynamics in nonintegrable quantum systems.

This talk is based on arXiv:2604.11015.

Speaker: Chihiro Matsui (University of Tokyo)

15:00 → 15:30 Tea break

15:30 → 16:30 Steady-state structures in open quantum systems beyond time-independence

Recent experimental developments in quantum simulators and quantum computers have enabled us to investigate the effects of measurement and dissipation on quantum dynamics. Theoretically, such open quantum systems are often analyzed in terms of the spectra and symmetries of the generators governing the dynamics, provided that the generators are time independent. However, it remains unclear how to analyze open quantum systems governed by time-dependent generators. In this talk, I discuss two topics concerning steady-state structures in open quantum systems beyond time-independent settings.

First, we consider measurement-induced phase transitions, where the dynamics of quantum trajectories cannot be described by time-independent generators because of random measurement outcomes. It is known that measurements in quantum many-body systems can lead to entanglement transitions in quantum trajectories. We show that this transition is accompanied by a spectral transition [1], in analogy with ground-state quantum phase transitions in equilibrium. Here, the relevant spectrum is defined as the Lyapunov spectrum, rather than the eigenvalue spectrum of a time-independent Hamiltonian. We discuss how the Lyapunov spectrum can be useful for characterizing open quantum systems that are not governed by time-independent generators [2–5].

Second, we consider a rigorous classification of steady-state dynamics in time-dependent Gorini-Kossakowski-Sudarshan-Lindblad equations with a recurrence property [6]. We introduce two distinct notions of strong symmetry, namely strong symmetries in the Schrödinger and Heisenberg pictures, and show that they completely characterize four different types of steady-state properties. We also discuss algebraic criteria for a system to have a unique steady state. We demonstrate our results in several examples, including time-quasiperiodically driven many-body systems.

[1] K. Mochizuki and RH, Phys. Rev. Lett. 134, 010410 (2025)
[1] K. Mochizuki and RH, Phys. Rev. Research 6 (1), 013004 (2024)
[1] K. Mochizuki and RH, J. Phys. A: Math. Theor. 58 (26), 265004 (2025)
[4] H. Oshima, K. Mochizuki, RH, Y. Fuji, Phys. Rev. Lett. 134 (24), 240401 (2025)
[5] RH et al., PTEP ptag055 (2026). [Review paper]
[6] H. Yoshida and RH, arXiv:2602.13095 (2026)

Speaker: Ryusuke Hamazaki (iTHEMS, RIKEN)

Tuesday 26 May

09:00 → 10:00 Nonperturbative Optics in Quantum Matter: Floquet, Schwinger, Berry, and Lorentz

Quantum materials demand a nonperturbative reformulation of optics: matrix-valued band Hamiltonians and quantum geometry replace the parabolic bands and optical Bloch framework of conventional semiconductor optics. I will organize this emerging field around four paradigms: Floquet engineering, dressing Bloch bands by periodic drives; Schwinger production, generalizing Zener tunneling to Dirac and Mott systems; Berry geometry, underlying anomalous and shift-current responses and threading through the others as their geometric backbone; and Lorentz boosts, which exploit the emergent Lorentz invariance of Dirac quasiparticles to recast spacetime-modulated drives in a co-moving frame[1]. Propagating waves then act as dynamical backgrounds for emergent relativistic field theories: subluminal drives yield topological spacetime crystals, while superluminal drives enter a nonperturbative regime hosting Cherenkov-type emission—rendering quantum materials a laboratory for nonequilibrium relativistic phenomena[2].
Reference:[1] TO, arXiv:2407.21458 (2024), [2] TO, Swati Chaudhary, in progress.

Speaker: Takashi Oka (Institute for Solid State Physics, University of Tokyo)

10:00 → 10:30 Tea break

10:30 → 11:30 Complex conformal field theory in non-Hermitian systems

Speaker: Kohei Kawabata (Institute for Solid State Physics, University of Tokyo)

11:30 → 13:00 Group photo + Lunch break

13:00 → 14:00 Extending Kibble-Zurek mechanism

The Kibble–Zurek mechanism (KZM) combines Kibble’s observation of topological defects formation in cosmological phase transitions with Zurek’s theory relating their density to critical slowing down, and hence to the universality class of a second-order phase transition. The resulting KZM predicts defect density as a function of the quench rate in second-order phase transitions, in both classical and quantum settings. It has applications across a wide range of fields, including condensed matter physics, cosmology, and quantum computing.

In this talk, I will discuss extensions of the Kibble–Zurek mechanism beyond its original formulation. I will explain how KZM can be combined with nucleation theory in weakly first-order phase transitions, how formulas for nonadiabatic excitations can be modified in exotic quantum phase transitions, and applications of machine learning that provide deeper insight into second-order phase transitions beyond the conventional KZM framework.

Speaker: Fumika Suzuki (University of Tokyo)

14:00 → 15:00 Several universal features in driven CFTs

In this talk, I will introduce our ongoing work on time-dependent driven CFTs in (1+1) dimensions. I will discuss several universal features that can be studied analytically, including the quantized acceleration of pseudo-entropy in quasi-periodically driven CFTs, as well as how conformal defects influence entanglement dynamics in driven CFTs. If time permits, I will also present our recent efforts on understanding the effects of dissipation in CFTs.

Speaker: Xueda Wen (Georgia Institute of Technology)

15:00 → 15:30 Tea break

15:30 → 16:30 Sigma-models with local couplings and integrability

Sigma-models are a class of quantum field theories that play an important role in many areas of physics, from string theory, to condensed matter, to pions. In two dimensions, particular choices of sigma-models are known to be integrable, or exactly solvable. I will present our results with Ben Hoare and Arkady Tseytlin on what happens if the couplings of integrable sigma-models are promoted to become spacetime dependent. Our finding across many examples is that the spacetime dependence apparently preserves classical integrability precisely when the dependence is according to the 1-loop renormalization group (RG) equation of the same theory. This statement is a surprising classical—quantum relation between classical integrability and the 1-loop RG flow. I will review interesting links between these spacetime dependent models and (i) string backgrounds built from the same sigma-model and (ii) 4d gravity reduced along two isometries. Finally, I will comment on relations to ongoing developments in the field.
[Based on 2008.01112]

Speaker: Nat Levine (University of Amsterdam)

Wednesday 27 May

09:00 → 10:00 Time-dependent sigma models from 4d Chern-Simons

In this talk, I will explain how to construct integrable sigma models with time-dependent couplings from 4d Chern-Simons. I will start by reviewing the basics of integrable sigma models, as well as the appropriate modifications to accommodate time-dependent coupling parameters. The main goal of this talk will be to present some useful frameworks for studying these integrable systems. At the forefront will be 4d Chern-Simons — a holomorphic-topological gauge theory which describes 2d integrable systems. If time permits, I may also touch on applications of twistor theory and 6d holomorphic Chern-Simons in this context.

Speaker: Lewis Cole (University of Edinburgh)

10:00 → 10:30 Tea break

10:30 → 11:30 Spacetime-dependent integrability from gauge theory

How should we define integrability in spacetime-dependent field theories? In this talk, I will argue that one needs to relax the Lax equation in a way that still renders the theory solvable. I will then show how this modified equation naturally arises from a modified version of four dimensional Chern-Simons Theory, which is known to generate many two dimensional integrable field theories. This makes it possible to find spacetime-dependent versions of most integrable models, which I will demonstrate in various examples.

Speaker: Anders Wallberg (École Polytechnique Fédérale de Lausanne)

11:30 → 13:00 Lunch break

13:00 → 14:00 Hydrodynamic fluctuations in integrable systems

Fluctuations at hydrodynamic scales encapsulate invaluable information about the dynamics in many-body systems. While such hydrodynamic fluctuations in non-integrable systems are well-understood and machineries for describing them have been established, it was recently realised that those in integrable systems are of a fundamentally different nature.

In this talk, I will explain how hydrodynamic fluctuations differ between non-integrable and integrable systems and introduce a formalism to evaluate these fluctuations in integrable systems. I will then illustrate one instance where the difference gives rise to an unconventional phenomenon: anomalous fluctuations in the XXZ spin chain.

Speaker: Takato Yoshimura (King’s College London)

14:00 → 15:00 Deconfined quantum criticality and non-invertible translation from Lieb–Schultz–Mattis anomaly

Speaker: Hiromi Ebisu (iTHEMS, RIKEN)

15:00 → 15:30 Tea break

15:30 → 16:30 Higher-Dimensional Black Holes from 2D Space-Dependent Integrable Sigma Models

In higher-dimensional gravity, black hole horizon topology is not restricted to spherical topology, and the systematic construction of exact solutions remains an important challenge.

In this talk, I explain how, under sufficient spacetime symmetries, higher-dimensional gravity reduces to a 2d space-dependent sigma model whose integrability enables exact solution construction. Using the monodromy matrix of the Breitenlohner–Maison linear system and the associated Riemann–Hilbert problem, I show how 5d vacuum solutions such as the Myers–Perry black hole, black ring, and black lens can be described and reconstructed in a unified way. I also discuss prospects for classifying non-spherical black holes and finding new exact solutions.

This talk is mainly based on joint work (hep-th/2510.02093) with Shinya Tomizawa of Toyota Technological Institute.

Speaker: Junichi Sakamoto (University of Osaka)