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 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.
Highlights
In this work we present a thorough analysis of the partitioning protocol for the transverse field Ising model, a paradigmatic integrable quantum spin chain
In this paper we studied the out of equilibrium evolution of the transverse field Ising model in the partitioning protocol when the initial state is the tensor product of two states with different macroscopic properties
Our results are directly applicable to initial states with vanishing anomalous fermionic correlations
Summary
The last decade witnessed an ever increasing interest in the out of equilibrium dynamics of quantum many-body systems [1, 2]. In this work we present a thorough analysis of the partitioning protocol for the transverse field Ising model, a paradigmatic integrable quantum spin chain This system can be mapped to free fermions, which makes it possible to give a microscopic derivation of the space-time profiles in inhomogeneous quenches. We go beyond the hydrodynamic scaling limit by computing the leading corrections to the NESS corresponding to the late time approach to the steady state These corrections are very difficult to determine in general, and the Ising model gives us the rare opportunity to derive them analytically. Details of the calculations and plots in support of the analytical results are collected in the appendices
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