Distilling momentum-space entanglement in Luttinger liquids at finite temperature

TL;DR

This paper explores the entanglement properties of reduced thermal density matrices in Luttinger liquids at finite temperature, revealing universal features and the persistence of an entanglement gap up to certain temperatures.

Contribution

It provides analytical and numerical insights into the momentum-space entanglement spectrum and Hamiltonian of Luttinger liquids at finite temperature, highlighting universality and temperature effects.

Findings

Presence of an entanglement gap up to certain temperatures

Momentum-space entanglement carried by high energy modes with flat spectrum

Von-Neumann entropy increases with temperature with a universal coefficient

Abstract

While much is known about the entanglement characteristics of ground states, the properties of reduced thermal density matrices have received significantly less attention. Here we investigate the entanglement content of reduced thermal density matrices for momentum-space bipartitioning in Luttinger liquids using analytical and numerical methods. The low lying part of its spectrum contains an "entanglement gap", which persists up to temperatures comparable to the level spacing. With increasing temperature, the low energy modes acquire dispersion and resemble to those in the physical Hamiltonian with an enhanced effective temperature. The momentum-space entanglement is carried by high energy modes (compared to temperature), featuring a completely flat spectrum. The von-Neumann entropy increases with temperature with a universal Sommerfeld coefficient. The momentum-space entanglement Hamiltonian turns out to be as universal as the physical Hamiltonian.