Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2606.20850

Hydrodynamic tails in chaotic spin chains with quantum group symmetry

Luca V. Delacretaz, Victor Gorbenko, Jiaozi Wang, Bernardo Zan, Aleksandr Zhabin

cond-mat.stat-mechcond-mat.str-elhep-thquant-phSubmitted Jun 18, 2026• Announced Jun 22, 2026• 0 citations
arXivHTMLPDF

Abstract

The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics -- such as superdiffusion -- in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying $U(1)$ charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.

Comments
15 pages, 18 figures

Related papers

Long-lived local coherences at high temperature from frozen domain walls

Sarang Gopalakrishnan, Romain Vasseur

Local coherences between distinct charge sectors--measured by the single-particle Green's function or the transverse spin autocorrelation function--do not overlap with hydrodynamic modes. At finite temperature, therefore, they decay faster than any power law in generic chaotic systems. We present a mechanism by which these coherences can persist anomalously long, for integrable and chaotic spin chains (including the XXZ and Fredkin spin chains) that obey a quantum group symmetry. We show--using a Mazur bound derived from the quantum-group symmetry, together with locality and a "non-undershoot" assumption--that the transverse spin autocorrelation function $C(t) \equiv \langle σ^-_x(t) σ^+_x(0)\rangle$ can decay at most algebraically: $C(t) \gtrsim 1/t^2$. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute $C(t) \sim \sqrt{3}/(18 \sqrt{t})$. We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as $C(t) \sim t^{-2/z}$ (for transport exponent $z$) in the chaotic models.

cond-mat.stat-mechCross-listedarXiv:2610.20724•Oct 16, 2026•0 citations

New symmetries in spin chains and quantum field theories

Zhabin, Aleksandr

This thesis studies Quantum Field Theories (QFTs) and many-body systems that have quantum groups as global internal symmetries. We establish that quantum groups can act as genuine global symmetries, constraining the spectrum, correlation functions and dynamics. Operators that transform naturally under this symmetry are shown to be non-local, living at the ends of topological lines that carry some novel properties. These properties are illustrated by explicit examples including spin chains and their field-theoretic continuum limit. We solve the continuum theory in two ways: first, by using constraints coming from quantum group symmetry together with conformal bootstrap techniques; second, by applying the Coulomb gas formalism. We further show that this symmetry is not an artifact of integrability: it survives as a global symmetry even when integrability is broken and the system becomes chaotic. Finally, we observe that it governs late-time hydrodynamic transport, as manifest in the slow decay of the transverse spin autocorrelation function. Altogether, these results position quantum groups as a new and robust class of symmetry governing the physics of QFTs and many-body systems.

•Jan 1, 2026•0 citations

Superuniversality of Superdiffusion

Enej Ilievski, Jacopo De Nardis, Sarang Gopalakrishnan +2 more

Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-Abelian global symmetry.This work offers a comprehensive group-theoretic account of this elusive phenomenon.For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group G, we find that finite-temperature transport of Noether charges associated with symmetry G in thermal states that are invariant under G is universally superdiffusive and characterized by the dynamical exponent z ¼ 3=2.This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it "superuniversal."The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations.We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters.We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua.Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.

arXiv:2009.08425•Physical Review X•Jul 28, 2021•96 citations

Anomalous transport from hot quasiparticles in interacting spin chains

Sarang Gopalakrishnan, Romain Vasseur

Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.

arXiv:2208.11133•Reports on Progress in Physics•Jan 16, 2023•39 citations

Emergent anomalous hydrodynamics at infinite temperature in a long-range XXZ model

Ang Yang, Jin-Lou Ma, Lei Ying

The conventional wisdom suggests that transports of conserved quantities in nonintegrable quantum many-body systems at high temperatures are diffusive. Recent study suggests a potential counterexample of this paradigm. We independently complement this counterexample by directly uncovering anomalous infinite-temperature hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. This model, classified as nonintegrable due to its Wigner-Dyson level-spacing statistics in the random matrix theory, exhibits a surprising superdiffusive-ballistic-superdiffusive transport transition by varying the power-law exponent of couplings for a fixed anisotropy. Our findings are verified by multiple observables, including the spin-spin autocorrelator, mean-square displacement, and spin conductivity. Interestingly, we further quantify the degree of quantum chaos using the Kullback-Leibler divergence between the entanglement entropy distributions of the model's eigenstates and a random state. Remarkably, an observed local maximum in the divergence near the transition boundary suggests a link between anomalous hydrodynamics and a suppression of quantum chaos. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of nonintegrable quantum many-body systems.

arXiv:2403.17912•Physical review. B./Physical review. B•Jul 16, 2024•3 citations

Anomalous spin transport in integrable random quantum circuits

Songlei Wang, Chenguang Liang, Hongzheng Zhao +1 more

High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.

cond-mat.stat-mechCross-listedarXiv:2602.09098•Feb 11, 2026•0 citations
The interplay between symmetry and thermalization governs the late-time dynamics of local quantum and classical many-body systems at nonzero temperature. Recently, two parallel frontiers have emerged: the search for robust anomalous hydrodynamics -- such as superdiffusion -- in generic, non-integrable models, and the formal effort to generalize the fundamental concept of global symmetry. In this paper, we bridge these frontiers by demonstrating that quantum group symmetry provides a novel mechanism for anomalous hydrodynamics in chaotic systems. We study the dynamics of local operators carrying U(1)U(1)U(1) charge in non-integrable lattice models that also have quantum group symmetry. One example is transverse spin in the XXZ model with integrability breaking deformations. While such excitations are expected to decay very quickly at high temperature because their charge forbids overlap with conventional hydrodynamic densities, we find that protection by the quantum group symmetry makes these modes long-lived, despite the absence of local quantum group charge density or current. Furthermore, the dynamics is superdiffusive across Hamiltonian, Floquet, and classical realizations, and exhibits unusual finite size effects at very late times. We also revisit transverse spin dynamics in the integrable XXZ model.
Local coherences between distinct charge sectors--measured by the single-particle Green's function or the transverse spin autocorrelation function--do not overlap with hydrodynamic modes. At finite temperature, therefore, they decay faster than any power law in generic chaotic systems. We present a mechanism by which these coherences can persist anomalously long, for integrable and chaotic spin chains (including the XXZ and Fredkin spin chains) that obey a quantum group symmetry. We show--using a Mazur bound derived from the quantum-group symmetry, together with locality and a "non-undershoot" assumption--that the transverse spin autocorrelation function C(t)≡⟨σx−(t)σx+(0)⟩C(t) \equiv \langle σ^-_x(t) σ^+_x(0)\rangleC(t)≡⟨σx−​(t)σx+​(0)⟩ can decay at most algebraically: C(t)≳1/t2C(t) \gtrsim 1/t^2C(t)≳1/t2. This bound is not tight: in the large-anisotropy limit of the XXZ spin chain, at infinite temperature, we explicitly compute C(t)∼3/(18t)C(t) \sim \sqrt{3}/(18 \sqrt{t})C(t)∼3​/(18t​). We also compute this decay rate in the XXZ spin chain for general easy-axis anisotropy, and estimate it to scale as C(t)∼t−2/zC(t) \sim t^{-2/z}C(t)∼t−2/z (for transport exponent zzz) in the chaotic models.
This thesis studies Quantum Field Theories (QFTs) and many-body systems that have quantum groups as global internal symmetries. We establish that quantum groups can act as genuine global symmetries, constraining the spectrum, correlation functions and dynamics. Operators that transform naturally under this symmetry are shown to be non-local, living at the ends of topological lines that carry some novel properties. These properties are illustrated by explicit examples including spin chains and their field-theoretic continuum limit. We solve the continuum theory in two ways: first, by using constraints coming from quantum group symmetry together with conformal bootstrap techniques; second, by applying the Coulomb gas formalism. We further show that this symmetry is not an artifact of integrability: it survives as a global symmetry even when integrability is broken and the system becomes chaotic. Finally, we observe that it governs late-time hydrodynamic transport, as manifest in the slow decay of the transverse spin autocorrelation function. Altogether, these results position quantum groups as a new and robust class of symmetry governing the physics of QFTs and many-body systems.
Anomalous finite-temperature transport has recently been observed in numerical studies of various integrable models in one dimension; these models share the feature of being invariant under a continuous non-Abelian global symmetry.This work offers a comprehensive group-theoretic account of this elusive phenomenon.For an integrable quantum model with local interactions, invariant under a global non-Abelian simple Lie group G, we find that finite-temperature transport of Noether charges associated with symmetry G in thermal states that are invariant under G is universally superdiffusive and characterized by the dynamical exponent z ¼ 3=2.This conclusion holds regardless of the Lie algebra symmetry, local degrees of freedom (on-site representations), Lorentz invariance, or particular realization of microscopic interactions: We accordingly dub it "superuniversal."The anomalous transport behavior is attributed to long-lived giant quasiparticles dressed by thermal fluctuations.We provide an algebraic viewpoint on the corresponding dressing transformation and elucidate formal connections to fusion identities amongst the quantum-group characters.We identify giant quasiparticles with nonlinear soliton modes of classical field theories that describe low-energy excitations above ferromagnetic vacua.Our analysis of these field theories also provides a complete classification of the low-energy (i.e., Goldstone-mode) spectra of quantum isotropic ferromagnetic chains.
Many experimentally relevant quantum spin chains are approximately integrable, and support long-lived quasiparticle excitations. A canonical example of integrable model of quantum magnetism is the XXZ spin chain, for which energy spreads ballistically, but, surprisingly, spin transport can be diffusive or superdiffusive. We review the transport properties of this model using an intuitive quasiparticle picture that relies on the recently introduced framework of generalized hydrodynamics. We discuss how anomalous linear response properties emerge from hierarchies of quasiparticles both in integrable and near-integrable limits, with an emphasis on the role of hydrodynamic fluctuations. We also comment on recent developments including non-linear response, full-counting statistics and far-from-equilibrium transport. We provide an overview of recent numerical and experimental results on transport in XXZ spin chains.
The conventional wisdom suggests that transports of conserved quantities in nonintegrable quantum many-body systems at high temperatures are diffusive. Recent study suggests a potential counterexample of this paradigm. We independently complement this counterexample by directly uncovering anomalous infinite-temperature hydrodynamics in a spin-1/2 XXZ chain with power-law couplings. This model, classified as nonintegrable due to its Wigner-Dyson level-spacing statistics in the random matrix theory, exhibits a surprising superdiffusive-ballistic-superdiffusive transport transition by varying the power-law exponent of couplings for a fixed anisotropy. Our findings are verified by multiple observables, including the spin-spin autocorrelator, mean-square displacement, and spin conductivity. Interestingly, we further quantify the degree of quantum chaos using the Kullback-Leibler divergence between the entanglement entropy distributions of the model's eigenstates and a random state. Remarkably, an observed local maximum in the divergence near the transition boundary suggests a link between anomalous hydrodynamics and a suppression of quantum chaos. This work offers another deep understanding of emergent anomalous transport phenomena in a wider range of nonintegrable quantum many-body systems.
High-temperature spin transport in integrable quantum spin chains exhibits a rich dynamical phase diagram, including ballistic, superdiffusive, and diffusive regimes. While integrability is known to survive in static and periodically driven systems, its fate in the complete absence of time-translation symmetry, particularly in interacting random quantum circuits, has remained unclear. Here we construct integrable random quantum circuits built from inhomogeneous XXZ R-matrices. Remarkably, integrability is preserved for arbitrary sequences of gate layers, ranging from quasiperiodic to fully random, thereby explicitly breaking both continuous and discrete time-translation symmetry. Using large-scale time-dependent density-matrix renormalization group simulations at infinite temperature and half filling, we map out the resulting spin-transport phase diagram and identify ballistic, superdiffusive, and diffusive regimes controlled by the spectral parameters of the R-matrices. The spatiotemporal structure of spin correlations within each regime depends sensitively on the inhomogeneity, exhibiting spatial asymmetry and sharp peak structures tied to near-degenerate quasiparticle velocities. To account for these findings, we develop a generalized hydrodynamics framework adapted to time-dependent integrable circuits, yielding Euler-scale predictions for correlation functions, Drude weights, and diffusion bounds. This approach identifies the quasiparticles governing transport and quantitatively captures both the scaling exponents and fine structures of the correlation profiles observed numerically. Our results demonstrate that exact Yang-Baxter integrability is compatible with stochastic quantum dynamics and establish generalized hydrodynamics as a predictive framework for transport in time-dependent integrable systems.