SciPost Physics

SciPost Phys. 3, 020 (2017) · published 8 September 2017

• doi: 10.21468/SciPostPhys.3.3.020
• pdf
• BiBTeX
• RIS
• Submissions/Reports
• 

Abstract

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 compute analytically 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.

• Bastianello et al., Nonequilibrium Steady State Generated by a Moving Defect: The Supersonic Threshold
  Phys. Rev. Lett. 120, 060602 (2018) [Crossref]
• Yoshinaga, Ballistic propagation of a local impact in the one-dimensional XY model
  J. Stat. Mech. 2021, 013103 (2021) [Crossref]
• Collura et al., Analytic solution of the domain-wall nonequilibrium stationary state
  Phys. Rev. B 97, 081111 (2018) [Crossref]
• Lancaster et al., Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains
  Phys. Rev. Research 1, 033104 (2019) [Crossref]
• Alba et al., Generalized-hydrodynamic approach to inhomogeneous quenches: correlations, entanglement and quantum effects
  J. Stat. Mech. 2021, 114004 (2021) [Crossref]
• De Nardis et al., Diffusion in generalized hydrodynamics and quasiparticle scattering
  SciPost Phys. 6, 049 (2019) [Crossref]
• Muralidharan et al., Generalized thermalization for integrable system under quantum quench
  Phys. Rev. E 97, 012142 (2018) [Crossref]
• Bocini, Connected correlations in partitioning protocols: A case study and beyond
  SciPost Phys. 15, 027 (2023) [Crossref]
• Roósz, Front dynamics in the Harper model
  Phys. Rev. B 109, 064204 (2024) [Crossref]
• Bastianello et al., From the sinh-Gordon field theory to the one-dimensional Bose gas: exact local correlations and full counting statistics
  J. Stat. Mech. 2018, 113104 (2018) [Crossref]
• Bertini et al., Transport in the sine-Gordon field theory: From generalized hydrodynamics to semiclassics
  Phys. Rev. B 100, 035108 (2019) [Crossref]
• Bastianello et al., Generalized Hydrodynamics with Space-Time Inhomogeneous Interactions
  Phys. Rev. Lett. 123, 130602 (2019) [Crossref]
• Ljubotina et al., Non-equilibrium quantum transport in presence of a defect: the non-interacting case
  SciPost Phys. 6, 004 (2019) [Crossref]
• Jin et al., Interplay between transport and quantum coherences in free fermionic systems
  J. Phys. A: Math. Theor. 54, 404001 (2021) [Crossref]
• Bulchandani et al., Subdiffusive front scaling in interacting integrable models
  Phys. Rev. B 99, 121410 (2019) [Crossref]
• Eisler et al., Front dynamics and entanglement in the XXZ chain with a gradient
  Phys. Rev. B 96, 174301 (2017) [Crossref]
• Fagotti, Locally quasi-stationary states in noninteracting spin chains
  SciPost Phys. 8, 048 (2020) [Crossref]
• Gouraud et al., Quench dynamics of noninteracting fermions with a delta impurity
  J. Phys. A: Math. Theor. 55, 395001 (2022) [Crossref]
• Bastianello et al., Superluminal moving defects in the Ising spin chain
  Phys. Rev. B 98, 064304 (2018) [Crossref]
• Alba, Towards a generalized hydrodynamics description of Rényi entropies in integrable systems
  Phys. Rev. B 99, 045150 (2019) [Crossref]
• Collura et al., Domain wall melting in the spin- 12 XXZ spin chain: Emergent Luttinger liquid with a fractal quasiparticle charge
  Phys. Rev. B 102, 180409 (2020) [Crossref]
• De Nardis et al., Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States
  Phys. Rev. Lett. 120, 217206 (2018) [Crossref]
• Mazza et al., Energy transport in an integrable parafermionic chain via generalized hydrodynamics
  Phys. Rev. B 98, 075421 (2018) [Crossref]
• Piroli et al., Transport in out-of-equilibrium XXZ chains: Nonballistic behavior and correlation functions
  Phys. Rev. B 96, 115124 (2017) [Crossref]
• Bertini et al., Universal Broadening of the Light Cone in Low-Temperature Transport
  Phys. Rev. Lett. 120, 176801 (2018) [Crossref]
• Mazza et al., Suppression of transport in nondisordered quantum spin chains due to confined excitations
  Phys. Rev. B 99, 180302 (2019) [Crossref]
• Ghosh et al., Disorder-induced enhancement of entanglement growth in one dimension: Information leakage at the scale of the localization length
  Phys. Rev. B 103, 024202 (2021) [Crossref]
• McRoberts et al., Domain Wall Dynamics in Classical Spin Chains: Free Propagation, Subdiffusive Spreading, and Soliton Emission
  Phys. Rev. Lett. 132, 057202 (2024) [Crossref]
• Doyon, Exact large-scale correlations in integrable systems out of equilibrium
  SciPost Phys. 5, 054 (2018) [Crossref]
• Kormos et al., Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench
  Phys. Rev. E 98, 032105 (2018) [Crossref]
• Horváth, Hydrodynamics of massless integrable RG flows and a non-equilibrium c-theorem
  J. High Energ. Phys. 2019, 20 (2019) [Crossref]
• Gouraud et al., Stationary time correlations for fermions after a quench in the presence of an impurity
  EPL 142, 41001 (2023) [Crossref]
• Eisler, Entanglement negativity in a nonequilibrium steady state
  Phys. Rev. B 107, 075157 (2023) [Crossref]
• Kirkby et al., Quantum caustics and the hierarchy of light cones in quenched spin chains
  Phys. Rev. Research 1, 033135 (2019) [Crossref]
• Ohanesjan et al., Energy dynamics, information and heat flow in quenched cooling and the crossover from quantum to classical thermodynamics
  J. High Energ. Phys. 2023, 237 (2023) [Crossref]
• Dutta et al., Generating symmetry-protected long-range entanglement
  Phys. Rev. Research 6, L012039 (2024) [Crossref]
• Ghosh et al., Magnetization dynamics in the XX spin chain model via multiparticle state
  Phys. Rev. B 104, 144306 (2021) [Crossref]
• De Nardis et al., Hydrodynamic Diffusion in Integrable Systems
  Phys. Rev. Lett. 121, 160603 (2018) [Crossref]
• Bertini et al., Finite-temperature transport in one-dimensional quantum lattice models
  Rev. Mod. Phys. 93, 025003 (2021) [Crossref]
• Eisler et al., Front dynamics in the XY chain after local excitations
  SciPost Phys. 8, 037 (2020) [Crossref]
• Alba, Entanglement and quantum transport in integrable systems
  Phys. Rev. B 97, 245135 (2018) [Crossref]
• Perfetto et al., Dynamics of large deviations in the hydrodynamic limit: Noninteracting systems
  Phys. Rev. E 102, 042128 (2020) [Crossref]
• Bertini et al., Low-temperature transport in out-of-equilibrium XXZ chains
  J. Stat. Mech. 2018, 033104 (2018) [Crossref]
• Perfetto et al., Euler-scale dynamical fluctuations in non-equilibrium interacting integrable systems
  SciPost Phys. 10, 116 (2021) [Crossref]
• Modak et al., Quantum adiabatic protocols using emergent local Hamiltonians
  Phys. Rev. E 96, 042155 (2017) [Crossref]
• Fagotti, Higher-order generalized hydrodynamics in one dimension: The noninteracting test
  Phys. Rev. B 96, 220302 (2017) [Crossref]
• Eisler et al., Hydrodynamical phase transition for domain-wall melting in the XY chain
  Phys. Rev. B 98, 161117 (2018) [Crossref]
• Bastianello et al., Integrability-Protected Adiabatic Reversibility in Quantum Spin Chains
  Phys. Rev. Lett. 122, 240606 (2019) [Crossref]
• De Nardis et al., Particle-hole pairs and density–density correlations in the Lieb–Liniger model
  J. Stat. Mech. 2018, 033102 (2018) [Crossref]
• Davis et al., Fractionalization Waves in Two-Dimensional Dirac Fermions: Quantum Imprint from One Dimension
  Phys. Rev. Lett. 122, 065302 (2019) [Crossref]
• Panfil et al., Linearized regime of the generalized hydrodynamics with diffusion
  SciPost Phys. Core 1, 002 (2019) [Crossref]
• Riddell et al., Scaling at the out-of-time-ordered correlator wavefront: Free versus chaotic models
  Phys. Rev. B 108, L121108 (2023) [Crossref]
• Ferro et al., Non-equilibrium entanglement asymmetry for discrete groups: the example of the XY spin chain
  J. Stat. Mech. 2024, 023101 (2024) [Crossref]
• Fremling et al., Dynamics and level statistics of interacting fermions in the lowest Landau level
  New J. Phys. 20, 103036 (2018) [Crossref]
• Gruber et al., Magnetization and entanglement after a geometric quench in the XXZ chain
  Phys. Rev. B 99, 174403 (2019) [Crossref]
• Fischer et al., Energy transport between critical one-dimensional systems with different central charges
  Phys. Rev. B 101, 205146 (2020) [Crossref]
• Zhang et al., Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
  Phys. Rev. A 99, 063605 (2019) [Crossref]
• Manna et al., Thermal Drude weight in an integrable chiral clock model
  Phys. Rev. B 108, 054304 (2023) [Crossref]