Entanglement R\'enyi entropy and boson-fermion duality in massless Thirring model

TL;DR

This paper computes the second Rényi entropy for two intervals in the massless Thirring model using boson-fermion duality, deriving exact results and analyzing how entanglement depends on interval size and coupling.

Contribution

It provides the first exact calculation of the second Rényi entropy in the massless Thirring model via boson-fermion duality, linking fermionic and bosonic descriptions.

Findings

Second Rényi entropy depends on interval sizes and coupling constant.

Mutual Rényi information increases with coupling strength.

Exact analytical and numerical results derived for the entropy.

Abstract

We investigate the second R\'enyi entropy of two intervals in the massless Thirring model describing a self-interacting Dirac fermion in two dimensions. Boson-fermion duality relating this model to a free compact boson theory enables us to simplify the calculation of the second R\'enyi entropy, reducing it to the evaluation of the partition functions of the bosonic theory on a torus. We derive exact results on the second R\'enyi entropy, and examine the dependence on the sizes of the intervals and the coupling constant of the model both analytically and numerically. We also explore the mutual R\'enyi information, a measure quantifying the correlation between the two intervals, and find that it generally increases as the coupling constant of the Thirring model becomes larger.