Spatial entanglement entropy in the ground state of the Lieb-Liniger model

TL;DR

This paper numerically investigates the spatial entanglement entropy in the ground state of the Lieb-Liniger model of interacting bosons, confirming theoretical scaling laws and computing non-universal constants across interaction regimes.

Contribution

The authors extend a replica-based quantum Monte Carlo method to efficiently compute spatial entanglement entropy in the Lieb-Liniger model, providing new numerical insights.

Findings

Logarithmic scaling of Rènyi entropy with subsystem size consistent with conformal field theory.

Computed non-universal constants for various interaction strengths.

Agreement with free fermion results in the strongly interacting limit.

Abstract

We consider the entanglement between two spatial subregions in the Lieb-Liniger model of bosons in one spatial dimension interacting via a contact interaction. Using ground state path integral quantum Monte Carlo we numerically compute the R\'{e}nyi entropy of the reduced density matrix of the subsystem as a measure of entanglement. Our numerical algorithm is based on a replica method previously introduced by the authors, which we extend to efficiently study the entanglement of spatial subsystems of itinerant bosons. We confirm a logarithmic scaling of the R\'{e}nyi entropy with subsystem size that is expected from conformal field theory, and compute the non-universal subleading constant for interaction strengths ranging over two orders of magnitude. In the strongly interacting limit, we find agreement with the known free fermion result.