Nonequilibrium current-carrying steady states in the anisotropic $XY$ spin chain

Abstract

Out-of-equilibrium behavior is explored in the one-dimensional anisotropic $XY$ model. Initially preparing the system in the isotropic $XX$ model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.

typos corrected, references added

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Cited by in corpus (14)

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• Expansion of one-dimensional lattice hard-core bosons at finite temperature
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• Exact large deviation function of spin current for the one dimensional XX spin chain with domain wall initial condition
• Front dynamics in the XY chain after local excitations
• Quantum dynamics of impenetrable SU(N) fermions in one-dimensional lattices
• Dynamics and level statistics of interacting fermions in the Lowest Landau Level
• Quantum adiabatic protocols using emergent local Hamiltonians
• Domain wall dynamics in classical spin chains: free propagation, subdiffusive spreading, and soliton emission
• Fractionalization Waves in Two-dimensional Dirac Fermions: Quantum Imprint from One Dimension
• Non-Equilibrium Steady State of the Lieb-Liniger model: exact treatment of the Tonks Girardeau limit
• Persistence of power-law correlations in nonequilibrium steady states of gapped quantum spin chains