R\'enyi entanglement entropies for the compactified massless boson with open boundary conditions

TL;DR

This paper derives explicit formulas for Re9nyi entanglement entropies in a 1D massless free boson system with open boundaries, including inhomogeneities, using advanced mathematical techniques.

Contribution

It provides new analytical expressions for Re9nyi entropies in open boundary conditions with inhomogeneities, extending previous homogeneous results.

Findings

Explicit Fredholm determinant-like formulas for Re9nyi entropies.

Reduction to linear integral equations and Riemann Theta functions in homogeneous cases.

Results applicable to generic bipartitions of the system.

Abstract

We investigate the R\'enyi entanglement entropies for the one-dimensional massless free boson compactified on a circle, which describes the low energy sector of several interacting many-body 1d systems (Luttinger Liquid). We focus on systems on a finite segment with open boundary conditions and possible inhomogeneities in the couplings. We provide expressions for the R\'enyi entropies of integer indices in terms of Fredholm determinant-like expressions. Within the homogeneous case, we reduce the problem to the solution of linear integral equations and the computation of Riemann Theta functions. We mainly focus on a single interval in the middle of the system, but results for generic bipartitions are given as well.