Universal parity effects in the entanglement entropy of XX chains with open boundary conditions

TL;DR

This paper analyzes the entanglement entropy in XX spin chains with open boundaries, deriving asymptotic behaviors and corrections using mathematical theorems and conformal field theory, applicable to both semi-infinite and finite systems.

Contribution

It provides a rigorous derivation of the asymptotic behavior and corrections of entanglement entropy in open XX chains, extending previous results with new mathematical and theoretical insights.

Findings

Asymptotic behavior of entanglement entropy derived for large blocks.

Exact correction terms characterized at order o(1/l).

Results applicable to both semi-infinite and finite chains.

Abstract

We consider the Renyi entanglement entropies in the one-dimensional XX spin-chains with open boundary conditions in the presence of a magnetic field. In the case of a semi-infinite system and a block starting from the boundary, we derive rigorously the asymptotic behavior for large block sizes on the basis of a recent mathematical theorem for the determinant of Toeplitz plus Hankel matrices. We conjecture a generalized Fisher-Hartwig form for the corrections to the asymptotic behavior of this determinant that allows the exact characterization of the corrections to the scaling at order o(1/l) for any n. By combining these results with conformal field theory arguments, we derive exact expressions also in finite chains with open boundary conditions and in the case when the block is detached from the boundary.