Finite-size corrections vs. relaxation after a sudden quench

TL;DR

This paper investigates finite-size effects on the relaxation dynamics and time averages of correlation functions and entanglement entropies after sudden quenches in translationally invariant Hamiltonians, highlighting the role of conservation laws.

Contribution

It introduces a method to compute leading finite-size corrections and analyzes how conservation laws influence relaxation and equilibration in finite quantum systems.

Findings

Time averages match infinite chain limits for local observables in noninteracting models.

Nonlocal operators show deviations due to conservation laws.

Large finite-size corrections are linked to slow relaxation dynamics.

Abstract

We consider the time evolution after sudden quenches of global parameters in translational invariant Hamiltonians and study the time average expectation values and entanglement entropies in finite chains. We show that in noninteracting models the time average of spin correlation functions is asymptotically equal to the infinite time limit in the infinite chain, which is known to be described by a generalized Gibbs ensemble. The equivalence breaks down considering nonlocal operators, and we establish that this can be traced back to the existence of conservation laws common to the Hamiltonian before and after the quench. We develop a method to compute the leading finite-size correction for time average correlation functions and entanglement entropies. We find that large corrections are generally associated to observables with slow relaxation dynamics.