R\'enyi entropies for one-dimensional quantum systems with mixed boundary conditions

TL;DR

This paper develops a method to compute Re9nyi entropies in one-dimensional critical quantum systems with mixed boundary conditions using conformal field theory, providing explicit formulas and finite size corrections.

Contribution

It introduces a general conformal field theory approach for Re9nyi entropies with mixed boundaries and derives explicit formulas for the second Re9nyi entropy in minimal models.

Findings

Explicit second Re9nyi entropy formula for minimal models.

Derived differential equations for correlation functions.

Compared theoretical results with numerical data for Ising and Potts chains.

Abstract

We present a general method for calculating R\'enyi entropies in the ground state of a one-dimensional critical system with mixed open boundaries, for an interval starting at one of its ends. In the conformal field theory framework, this computation boils down to the evaluation of the correlation function of one twist field and two boundary condition changing operators in the cyclic orbifold. Exploiting null-vectors of the cyclic orbifold, we derive ordinary differential equations satisfied by these correlation functions. In particular, we obtain an explicit expression for the second R\'enyi entropy valid for any diagonal minimal model, but with a particular set of mixed boundary conditions. In order to compare our results with numerical data for the Ising and three-state Potts critical chains, we also identify and compute the leading finite size corrections.