Stationary entropies after a quench from excited states in the Ising chain

TL;DR

This paper investigates the long-term entropies of the transverse field Ising chain after a sudden quench from excited states, revealing a consistent ratio between different entropy measures and emphasizing careful thermodynamic limit extraction.

Contribution

It provides a detailed analysis of stationary entropies after a quench from excited states, highlighting the relationship between generalized Gibbs and diagonal ensemble entropies.

Findings

Generalized Gibbs entropy is always twice the diagonal entropy.

Different microstate averages can lead to different entropy results.

Careful consideration is needed when extracting the thermodynamic limit.

Abstract

We consider the asymptotic state after a sudden quench of the magnetic field in the transverse field quantum Ising chain starting from excited states of the pre-quench Hamiltonian. We compute the thermodynamic entropies of the generalised Gibbs and the diagonal ensembles and we find that the generalised Gibbs entropy is always twice the diagonal one. We show that particular care should be taken in extracting the thermodynamic limit since different averages of equivalent microstates give different results for the entropies.