Subsystem distances between quasiparticle excited states

TL;DR

This paper studies how subsystem distances between quasiparticle excited states behave in various integrable models, revealing universal decoupling conditions related to energy and momentum differences.

Contribution

It introduces a universal quasiparticle picture for subsystem distances, valid across free and interacting integrable models, based on large energy and momentum difference conditions.

Findings

Subsystem distances decouple when quasiparticles have large energy.

Subsystem distances decouple when quasiparticles have large momentum difference.

Subsystem mode method efficiently computes subsystem distances, applicable to multiple models.

Abstract

We investigate the subsystem Schatten distance, trace distance and fidelity between the quasiparticle excited states of the free and the nearest-neighbor coupled fermionic and bosonic chains and the ferromagnetic phase of the spin-1/2 XXX chain. The results support the scenario that in the scaling limit when one excited quasiparticle has a large energy it decouples from the ground state and when two excited quasiparticles have a large momentum difference they decouple from each other. From the quasiparticle picture, we get the universal subsystem distances that are valid when both the large energy condition and the large momentum difference condition are satisfied, by which we mean each of the excited quasiparticles has a large energy and the momentum difference of each pair of the excited quasiparticles is large. In the free fermionic and bosonic chains, we use the subsystem mode method and get efficiently the subsystem distances, which are also valid in the coupled fermionic and bosonic chains if the large energy condition is satisfied. Moreover, under certain limit the subsystem distances from the subsystem mode method are even valid in the XXX chain. We expect that the results can be also generalized for other integrable models.