Estimating Quasi-long-range Order via Renyi Entropies

TL;DR

This paper demonstrates how Rènyi entropies can be used to estimate quasi-long-range order in one-dimensional systems, validated on known models and applied to phase transitions and multispecies systems.

Contribution

It establishes a direct relationship between the Luttinger parameter and Rènyi entropies across bosonic and fermionic lattice models, providing a new method for analyzing quantum phases.

Findings

Accurate estimation of quasi-long-range order using Rènyi entropies in the XXZ chain.

Efficient detection of phase transitions like superfluid-charge density wave transition.

First proof of the link between Luttinger parameter and Rènyi entropies in lattice models.

Abstract

We show how entanglement entropies allow for the estimation of quasi-long-range order in one dimensional systems whose low-energy physics is well captured by the Tomonaga-Luttinger liquid universality class. First, we check our procedure in the exactly solvable XXZ spin-1/2 chain in its entire critical region, finding very good agreement with Bethe ansatz results. Then, we show how phase transitions between different dominant orders may be efficiently estimated by considering the superfluid-charge density wave transition in a system of dipolar bosons. Finally, we discuss the application of this method to multispecies systems such as the one dimensional Hubbard model. Our work represent the first proof of a direct relationship between the Luttinger parameter and R\'enyi entropies in both bosonics and fermionic lattice models.