Second R\'enyi entropy and annulus partition function for one-dimensional quantum critical systems with boundaries

TL;DR

This paper derives an exact formula for the second R'enyi entropy in boundary-critical 1D quantum systems using the annulus partition function, validated by numerical results for the quantum Ising chain.

Contribution

It provides a new exact analytical expression for entanglement entropy in boundary-critical systems, connecting it to the annulus partition function.

Findings

Exact formula matches numerical data for the quantum Ising chain.

Finite-size corrections are significant and analyzed in detail.

Results enhance understanding of boundary effects on entanglement entropy.

Abstract

We consider the entanglement entropy in critical one-dimensional quantum systems with open boundary conditions. We show that the second R\'enyi entropy of an interval away from the boundary can be computed exactly, provided the same conformal boundary condition is applied on both sides. The result involves the annulus partition function. We compare our exact result with numerical computations for the critical quantum Ising chain with open boundary conditions. We find excellent agreement, and we analyse in detail the finite-size corrections, which are known to be much larger than for a periodic system.