Universal and nonuniversal contributions to block-block entanglement in many-fermion systems

TL;DR

This paper analyzes the entanglement entropy in many-fermion systems, identifying universal, nonuniversal, and finite-size contributions, with the nonuniversal term dominating in most cases, especially for larger blocks.

Contribution

It provides explicit expressions for the nonuniversal term in the 1D Hubbard model and compares analytical and numerical results to assess contribution significance.

Findings

Nonuniversal term dominates the entanglement entropy in most cases.

Finite-size corrections are negligible.

Universal Calabrese-Cardy term becomes significant for larger blocks.

Abstract

We calculate the entanglement entropy of blocks of size x embedded in a larger system of size L, by means of a combination of analytical and numerical techniques. The complete entanglement entropy in this case is a sum of three terms. One is a universal x and L-dependent term, first predicted by Calabrese and Cardy, the second is a nonuniversal term arising from the thermodynamic limit, and the third is a finite size correction. We give an explicit expression for the second, nonuniversal, term for the one-dimensional Hubbard model, and numerically assess the importance of all three contributions by comparing to the entropy obtained from fully numerical diagonalization of the many-body Hamiltonian. We find that finite-size corrections are very small. The universal Calabrese-Cardy term is equally small for small blocks, but becomes larger for x>1. In all investigated situations, however, the by far dominating contribution is the nonuniversal term steming from the thermodynamic limit.