Entanglement and diagonal entropies after a quench with no pair structure

TL;DR

This paper investigates how entanglement entropy evolves after a quantum quench in non-interacting fermions when the initial state generates multi-plet excitations instead of pairs, proposing a generalized formula for entropy dynamics.

Contribution

It introduces a new generalization of the semiclassical formula for entanglement entropy applicable to initial states with multi-plet excitations, extending understanding beyond pair-structured quenches.

Findings

Standard semiclassical formula fails for multi-plet excitations.

The proposed generalized formula matches numerical data.

The ratio of thermodynamic to diagonal entropy varies between 1/2 and 1 depending on initial conditions.

Abstract

A typical working condition in the study of quantum quenches is that the initial state produces a distribution of quasiparticle excitations with an opposite-momentum-pair structure. In this work we investigate the dynamical and stationary properties of the entanglement entropy after a quench from initial states which do not have such structure: instead of pairs of excitations they generate $\nu$-plets of correlated excitations with $\nu>2$. Our study is carried out focusing on a system of non-interacting fermions on the lattice. We study the time evolution of the entanglement entropy showing that the standard semiclassical formula is not applicable. We propose a suitable generalisation which correctly describes the entanglement entropy evolution and perfectly matches numerical data. We finally consider the relation between the thermodynamic entropy of the stationary state and the diagonal entropy, showing that when there is no pair structure their ratio depends on the details of the initial state and lies generically between $1/2$ and $1$.