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:1706.00413 · Physical review. B./Physical review. B

Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions

Lorenzo Piroli, Jacopo De Nardis, Mario Collura, Bruno Bertini, Maurizio Fagotti

Published Sep 14, 2017• 193 citations
arXivHTMLPDF

Abstract

We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joined together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time-dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal nonballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of time-dependent density matrix renormalization group simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.

DOI
10.1103/physrevb.96.115124

Related papers

Low-temperature transport in out-of-equilibrium XXZ chains

Bruno Bertini, Lorenzo Piroli

We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of ζ for all local observables.

•Nov 13, 2018•47 citations

Low-temperature transport in out-of-equilibrium XXZ chains

Bruno Bertini, Lorenzo Piroli

Abstract We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio ζ = x / t . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ . We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width Δ ζ ∝ T emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of ζ for all local observables.

arXiv:1711.00519•Journal of Statistical Mechanics Theory and Experiment•Mar 1, 2018•45 citations

Transport in Out-of-Equilibrium X X Z Chains: Exact Profiles of Charges and Currents

Bruno Bertini, Mario Collura, Jacopo De Nardis +1 more

We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: (1) at different temperatures, (2) in the ground state of two different models, and (3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.

arXiv:1605.09790•Physical Review Letters•Nov 8, 2016•851 citations

Exact late-time dynamics of XXZ spin-$\frac{1}{2}$ chains starting from inhomogeneous initial states

Bruno Bertini, Mario Collura, Jacopo De Nardis +1 more

We consider the non-equilibrium time evolution of piece-wise homogeneous states in the XXZ \mbox{spin-$\frac{1}{2}$} chain, a paradigmatic example of interacting integrable models. The initial state can be thought as the result of joining chains with different global properties. Through dephasing, at late times the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation fulfilled by the root densities specifying the thermodynamics of the model. We focus here on the gapless phase of the model in the cases where the chains are prepared: 1) at different temperatures; 2) in the ground state of two different models. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on \textsc{tebd} algorithms. As a corollary, we deduce the expressions for the expectation values of the currents of conserved charges in any stationary state.

•May 31, 2016•0 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

Spin- 1/2 XXZ chain coupled to two Lindblad baths: Constructing nonequilibrium steady states from equilibrium correlation functions

Tjark Heitmann, Jonas Richter, Fengping Jin +7 more

State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-$1/2$ XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.

arXiv:2303.00430•Physical review. B./Physical review. B•Nov 27, 2023•6 citations
We consider the nonequilibrium protocol where two semi-infinite gapped XXZ chains, initially prepared in different equilibrium states, are suddenly joined together. At large times, a generalized hydrodynamic description applies, according to which the system can locally be represented by space- and time-dependent stationary states. The magnetization displays an unusual behavior: depending on the initial state, its profile may exhibit abrupt jumps that can not be predicted directly from the standard hydrodynamic equations and which signal nonballistic spin transport. We ascribe this phenomenon to the structure of the local conservation laws and make a prediction for the exact location of the jumps. We find that the jumps propagate at the velocities of the heaviest quasiparticles. By means of time-dependent density matrix renormalization group simulations we show that our theory yields a complete description of the long-time steady profiles of conserved charges, currents, and local correlations.
We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ. We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of ζ for all local observables.
Abstract We study the low-temperature transport properties of out-of-equilibrium XXZ spin-1/2 chains. We consider the protocol where two semi-infinite chains are prepared in two thermal states at small but different temperatures and suddenly joined together. We focus on the qualitative and quantitative features of the profiles of local observables, which at large times t and distances x from the junction become functions of the ratio ζ = x / t . By means of the generalized hydrodynamic equations, we analyse the rich phenomenology arising by considering different regimes of the phase diagram. In the gapped phases, variations of the profiles are found to be exponentially small in the temperatures, but described by non-trivial functions of ζ . We provide analytical formulae for the latter, which give accurate results also for small but finite temperatures. In the gapless regime, we show how the three-step conformal predictions for the profiles of energy density and energy current are naturally recovered from the hydrodynamic equations. Moreover, we also recover the recent non-linear Luttinger liquid predictions for low-temperature transport: universal peaks of width Δ ζ ∝ T emerge at the edges of the light cone in the profiles of generic observables. Such peaks are described by the same function of ζ for all local observables.
We consider the nonequilibrium time evolution of piecewise homogeneous states in the XXZ spin-1/2 chain, a paradigmatic example of an interacting integrable model. The initial state can be thought of as the result of joining chains with different global properties. Through dephasing, at late times, the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation which fully characterizes the thermodynamics of the model. We restrict ourselves to the gapless phase and consider cases where the chains are prepared: (1) at different temperatures, (2) in the ground state of two different models, and (3) in the "domain wall" state. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on time-evolving block decimation algorithms. As a corollary, we unveil an exact expression for the expectation values of the charge currents in a generic stationary state.
Exact late-time dynamics of XXZ spin-12\frac{1}{2}21​ chains starting from inhomogeneous initial states
We consider the non-equilibrium time evolution of piece-wise homogeneous states in the XXZ \mbox{spin-12\frac{1}{2}21​} chain, a paradigmatic example of interacting integrable models. The initial state can be thought as the result of joining chains with different global properties. Through dephasing, at late times the state becomes locally equivalent to a stationary state which explicitly depends on position and time. We propose a kinetic theory of elementary excitations and derive a continuity equation fulfilled by the root densities specifying the thermodynamics of the model. We focus here on the gapless phase of the model in the cases where the chains are prepared: 1) at different temperatures; 2) in the ground state of two different models. We find excellent agreement (any discrepancy is within the numerical error) between theoretical predictions and numerical simulations of time evolution based on \textsc{tebd} algorithms. As a corollary, we deduce the expressions for the expectation values of the currents of conserved charges in any stationary state.
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.
State-of-the-art approaches to extract transport coefficients of many-body quantum systems broadly fall into two categories: (i) they target the linear-response regime in terms of equilibrium correlation functions of the closed system; or (ii) they consider an open-system situation typically modeled by a Lindblad equation, where a nonequilibrium steady state emerges from driving the system at its boundaries. While quantitative agreement between (i) and (ii) has been found for selected model and parameter choices, also disagreement has been pointed out in the literature. Studying magnetization transport in the spin-1/21/21/2 XXZ chain, we here demonstrate that at weak driving, the nonequilibrium steady state in an open system, including its buildup in time, can remarkably be constructed just on the basis of correlation functions in the closed system. We numerically illustrate this direct correspondence of closed-system and open-system dynamics, and show that it allows the treatment of comparatively large open systems, usually only accessible to matrix product state simulations. We also point out potential pitfalls when extracting transport coefficients from nonequilibrium steady states in finite systems.