Entanglement of several blocks in fermionic chains

TL;DR

This paper introduces a new formula for calculating the entanglement entropy of multiple intervals in fermionic chains, supported by numerical validation and a conjecture on Toeplitz matrix behavior.

Contribution

It proposes a novel expression for entanglement entropy in fermionic chains and conjectures a new asymptotic formula for Toeplitz matrix sub-matrices.

Findings

Numerical validation confirms the accuracy of the proposed entanglement entropy expression.

Conjecture on the asymptotic behavior of Toeplitz matrix principal sub-matrices.

Potential implications for understanding quantum entanglement in fermionic systems.

Abstract

In this paper we propose an expression for the entanglement entropy of several intervals in a stationary state of a free, translational invariant Hamiltonian in a fermionic chain. We check numerically the accuracy of our proposal and conjecture a new formula for the asymptotic behaviour of principal sub-matrices of a Toeplitz matrix.