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:1704.03437 · Physical review. E

Ballistic front dynamics after joining two semi-infinite quantum Ising chains

Gabriele Perfetto, Andrea Gambassi

Published Jul 19, 2017• 71 citations
arXivHTMLPDF

Abstract

We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasiparticles which characterize the ensuing unitary dynamics. Within the so-called semiclassical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasiparticles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.

DOI
10.1103/physreve.96.012138

Related papers

Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics

Márton Kormos

We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.

arXiv:1704.03744•SciPost Physics•Sep 8, 2017•91 citations

Nonequilibrium thermal transport in the quantum Ising chain

Andrea De Luca, Jacopo Viti, Denis Bernard +1 more

We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.

arXiv:1305.4984•Physical Review B•Oct 14, 2013•106 citations

Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench

Márton Kormos, Cătălin Paşcu Moca, Gergely Zaránd

We use a semiclassical approach to study out-of-equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low-energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space- and time-dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a ``second front'' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of nontrivial scattering processes in the $O(3)$ nonlinear sigma model by performing Monte Carlo simulations, and we observe local equilibration around the second front in terms of the densities of the particle species.

arXiv:1712.09466•Physical review. E•Sep 4, 2018•24 citations

Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems

Gabriele Perfetto, Andrea Gambassi

We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of noninteracting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semiclassical picture of quasiparticles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of noninteracting fermions and bosons are discussed.

arXiv:2007.12113•Physical review. E•Oct 23, 2020•27 citations

Scaling and front dynamics in Ising quantum chains

Thierry Platini, Dragi Karevski

We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case Tb=∞ and Ts=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.

•Jan 1, 2005•34 citations

Ballistic transport and boundary resistances in inhomogeneous quantum spin chains

Alberto Biella, Mario Collura, Davide Rossini +2 more

Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.

arXiv:1905.00088•Nature Communications•Oct 23, 2019•29 citations
We consider two semi-infinite quantum Ising chains initially at thermal equilibrium at two different temperatures and subsequently joined by an interaction between their end points. Transport properties such as the heat current are determined by the dynamics of the left- and right-moving fermionic quasiparticles which characterize the ensuing unitary dynamics. Within the so-called semiclassical space-time scaling limit we extend known results by determining the full space and time dependence of the density and current of energy and of fermionic quasiparticles. Upon approaching the edge of the propagating front, these quantities as well as the two-point correlation function display qualitatively different behaviors depending on the transverse field of the chain being critical or not. While in the latter case corrections to the leading behavior are described, as expected, by the Airy kernel, in the former a novel scaling form emerges with universal features.
We investigate the non-equilibrium dynamics of the transverse field quantum Ising chain evolving from an inhomogeneous initial state given by joining two macroscopically different semi-infinite chains. We obtain integral expressions for all two-point correlation functions of the Jordan--Wigner Majorana fermions at any time and for any value of the transverse field. Using this result, we analytically compute the profiles of various physical observables in the space-time scaling limit and show that they can be obtained from a hydrodynamic picture based on ballistically propagating quasiparticles. Going beyond the hydrodynamic limit, we analyze the approach to the non-equilibrium steady state and find that the leading late time corrections display a lattice effect. We also study the fine structure of the propagating fronts which are found to be described by the Airy kernel and its derivatives. Near the front we observe the phenomenon of energy back-flow where the energy locally flows from the colder to the hotter region.
We consider two quantum Ising chains initially prepared at thermal equilibrium but with different temperatures and coupled at a given time through one of their end points. In the long-time limit the system reaches a nonequilibrium steady state. We discuss properties of this nonequilibrium steady state and characterize the convergence to the steady regime. We compute the mean energy flux through the chain and show that the heat transport is ballistic. We derive also the large-deviation function for the quantum and thermal fluctuations of this energy transfer.
We use a semiclassical approach to study out-of-equilibrium dynamics and transport in quantum systems with massive quasiparticle excitations having internal quantum numbers. In the universal limit of low-energy quasiparticles, the system is described in terms of a classical gas of colored hard-core particles. Starting from an inhomogeneous initial state, in this limit we give analytic expressions for the space- and time-dependent spin density and spin current profiles. Depending on the initial state, the spin transport is found to be ballistic or diffusive. In the ballistic case we identify a ``second front'' that moves more slowly than the maximal quasiparticle velocity. Our analytic results also capture the diffusive broadening of this ballistically propagating front. To go beyond the universal limit, we study the effect of nontrivial scattering processes in the O(3)O(3)O(3) nonlinear sigma model by performing Monte Carlo simulations, and we observe local equilibration around the second front in terms of the densities of the particle species.
We study the dynamics of the statistics of the energy transferred across a point along a quantum chain which is prepared in the inhomogeneous initial state obtained by joining two identical semi-infinite parts thermalized at two different temperatures. In particular, we consider the transverse field Ising and harmonic chains as prototypical models of noninteracting fermionic and bosonic excitations, respectively. Within the so-called hydrodynamic limit of large space-time scales we first discuss the mean values of the energy density and current, and then, aiming at the statistics of fluctuations, we calculate exactly the scaled cumulant generating function of the transferred energy. From the latter, the evolution of the associated large deviation function is obtained. A natural interpretation of our results is provided in terms of a semiclassical picture of quasiparticles moving ballistically along classical trajectories. Similarities and differences between the transferred energy scaled cumulant and the large deviation functions in the cases of noninteracting fermions and bosons are discussed.
We study the relaxation behaviour of the quantum Ising chain, focusing our attention onto the non-equilibrium dynamics of the transverse magnetization. The initial states, from which the magnetization relaxes, are product states such as those generated by setting in contact several systems, each initially equilibrated at a given temperature. Due to the free fermionic structure of the chain, the dynamics of the transverse magnetization is easily expressed in a compact form. In the completely factorized initial state, corresponding to a situation where all the spins are thermalized independently, we obtain in the scaling limit the Green function associated to the transverse magnetization. The relaxation behaviour is also considered in the system-bath case, where part of the chain called the system is thermalized at a temperature Ts and the remaining part is at a temperature Tb. The magnetization profiles show a scaling behaviour. Moreover, in the extreme case Tb=∞ and Ts=0, it is shown that the magnetization relaxes in quantized steps in the strong transverse field region.
Transport phenomena are central to physics, and transport in the many-body and fully-quantum regime is attracting an increasing amount of attention. It has been recently revealed that some quantum spin chains support ballistic transport of excitations at all energies. However, when joining two semi-infinite ballistic parts, such as the XX and XXZ spin-1/2 models, our understanding suddenly becomes less established. Employing a matrix-product-state ansatz of the wavefunction, we study the relaxation dynamics in this latter case. Here we show that it takes place inside a light cone, within which two qualitatively different regions coexist: an inner one with a strong tendency towards thermalization, and an outer one supporting ballistic transport. We comment on the possibility that even at infinite time the system supports stationary currents and displays a non-zero Kapitza boundary resistance. Our study paves the way to the analysis of the interplay between transport, integrability, and local defects.