Scaling behaviour of the relaxation in quantum chains

Abstract

We consider the nonequilibrium time evolution of the transverse magnetization in the critical Ising and $XX$ quantum chains. For some inhomogeneously magnetized initial states we derive analytically the transverse magnetization profiles and show that they evolve into scaling forms in the long-time limit. In particular it is seen that the Ising chain exhibits some similarities with the conserved dynamics $XX$ chain. That is, after a transient regime, the total residual magnetization in the transverse direction is also conserved in the Ising case. A class of general initial states is also considered.

6 pages, 2 figures, accepted in EPJB

Cited by in corpus (38)

• Entanglement and correlation functions following a local quench: a conformal field theory approach
• Quantum Quenches in an XXZ Spin Chain from a Spatially Inhomogeneous Initial State
• Quantum quench from a thermal tensor state: boundary effects and generalized Gibbs ensemble
• Entanglement spreading after a geometric quench in quantum spin chains
• Relaxation in the XX quantum chain
• Entanglement evolution after connecting finite to infinite quantum chains
• Inhomogeneous quenches in the transverse field Ising chain: scaling and front dynamics
• Universal front propagation in the quantum Ising chain with domain-wall initial states
• Emergent eigenstate solution to quantum dynamics far from equilibrium
• Time evolution of 1D gapless models from a domain-wall initial state: SLE continued?
• Front dynamics and entanglement in the XXZ chain with a gradient
• Integrability-protected adiabatic reversibility in quantum spin chains
• Critical quench dynamics in confined systems
• Entangling many-body bound states with propagative modes in Bose-Hubbard systems
• Non-Equilibrium Steady State generated by a moving defect: the supersonic threshold
• Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
• Exact hydrodynamic solution of a double domain wall melting in the spin-1/2 XXZ model
• Dynamics of large deviations in the hydrodynamic limit: Non-interacting systems
• Exact hydrodynamic description of symmetry-resolved Rényi entropies after a quantum quench
• Emergent eigenstate solution and emergent Gibbs ensemble for expansion dynamics in optical lattices
• Front dynamics in the XY chain after local excitations
• Hydrodynamic description of Hard-core Bosons on a Galileo ramp
• Semiclassical theory of front propagation and front equilibration following an inhomogeneous quantum quench
• Nonequilibrium current-carrying steady states in the anisotropic $XY$ spin chain
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Superluminal moving defects in the Ising spin chain
• Thermalization dynamics close to a quantum phase transition
• Fourier's law on a one-dimensional optical random lattice
• Connected correlations in partitioning protocols: a case study and beyond
• Decoherence of Bell states by local interactions with a suddenly quenched spin environment
• Some speculations about local thermalization of nonequilibrium extended quantum systems
• Quasicondensation and off-diagonal long-range order of hard-core bosons during a free expansion
• Domain-wall melting and entanglement in free-fermion chains with a band structure
• Ballistic propagation of a local impact in the one-dimensional $XY$ model
• Domain-wall melting in all-to-all QSSEP from random-matrix theory
• Inhomogeneous quenches and GHD in the $\nu =1$ QSSEP model
• Entanglement dynamics of a hard-core quantum gas during a Joule expansion
• Entanglement Hamiltonian during a domain wall melting in the free Fermi chain