Shannon entropy in quasiparticle states of quantum chains

TL;DR

This paper analyzes Shannon entropy and mutual information in quasiparticle states of quantum chains, deriving analytical formulas and revealing universal behaviors and differences from entanglement entropy.

Contribution

It provides new analytical formulas for Shannon entropy in quasiparticle states and uncovers universal results and distinctions from entanglement entropy in large momentum difference limits.

Findings

Shannon entropy does not typically separate for quasiparticles with large momentum differences.

Universal quantum bosonic and fermionic results are obtained in the large momentum difference limit.

Analytical formulas are derived for single- and double-particle states in the scaling limit.

Abstract

We investigate the Shannon entropy of the total system and its subsystems, as well as the subsystem Shannon mutual information, in quasiparticle excited states of free bosonic and fermionic chains and the ferromagnetic phase of the spin-1/2 XXX chain. For single-particle and double-particle states, we derive various analytical formulas for free bosonic and fermionic chains in the scaling limit. These formulas are also applicable to certain magnon excited states in the XXX chain in the scaling limit. We also calculate numerically the Shannon entropy and mutual information for triple-particle and quadruple-particle states in bosonic, fermionic, and XXX chains. We discover that Shannon entropy, unlike entanglement entropy, typically does not separate for quasiparticles with large momentum differences. Moreover, in the limit of large momentum difference, we obtain universal quantum bosonic and fermionic results that are generally distinct and cannot be explained by a semiclassical picture.