Spin structures and entanglement of two disjoint intervals in conformal field theories

TL;DR

This paper analyzes the moments of reduced density matrices for two disjoint intervals in critical free fermionic models, linking lattice results to conformal field theory and spin structures, with numerical validation.

Contribution

It establishes a direct correspondence between lattice matrix moments and conformal field theory partition functions with specific spin structures in the scaling limit.

Findings

Analytical expressions match numerical results for Ising and XX chains.

Each term in the moments sum corresponds to a CFT partition function on Riemann surfaces.

The approach connects lattice models with conformal field theory through spin structures.

Abstract

We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two or four Gaussian matrices and hence their moments can be reconstructed as computable sums of products of Gaussian operators. We find that, in the scaling limit, each term in these sums is in one-to-one correspondence with the partition function of the corresponding conformal field theory on the underlying Riemann surface with a given spin structure. The analytical findings have been checked against numerical results for the Ising chain and for the XX spin chain at the critical point.