The entanglement entropy of 1D systems in continuous and homogenous space

TL;DR

This paper develops a systematic method to compute bipartite entanglement entropy in 1D quantum gases, revealing universal scaling behaviors and corrections for systems with and without boundaries.

Contribution

It introduces a new framework for calculating entanglement entropy in 1D quantum gases mapped to noninteracting fermions, including universal formulas for scaling and corrections.

Findings

Entanglement entropy scales as log N with system size.

Universal formulas for leading and subleading scaling corrections.

Applicability to ground and excited states in periodic and boundary systems.

Abstract

We introduce a systematic framework to calculate the bipartite entanglement entropy of a compact spatial subsystem in a one-dimensional quantum gas which can be mapped into a noninteracting fermion system. We show that when working with a finite number of particles N, the Renyi entanglement entropies grow as log N, with a prefactor that is given by the central charge. We apply this novel technique to the ground state and to excited states of periodic systems. We also consider systems with boundaries. We derive universal formulas for the leading behavior and for subleading corrections to the scaling. The universality of the results allows us to make predictions for the finite-size scaling forms of the corrections to the scaling.