Entanglement and area laws in weakly correlated gaussian states

TL;DR

This paper presents a method to evaluate entanglement measures in weakly correlated gaussian states, deriving simple asymptotic expressions and area laws for bipartitions and pairs of subsystems, with applications to lattice models.

Contribution

It introduces a novel approach to compute entanglement measures using singular values of a specific matrix block, simplifying the derivation of area laws in gaussian states.

Findings

Derived asymptotic expressions for entanglement entropy and negativity.

Established area laws depending on block orientation and separation.

Applied results to 2D lattice models with various couplings.

Abstract

We examine the evaluation of entanglement measures in weakly correlated gaussian states. It is shown that they can be expressed in terms of the singular values of a particular block of the generalized contraction matrix. This result enables to obtain in a simple way asymptotic expressions and related area laws for the entanglement entropy of bipartitions in pure states, as well as for the logarithmic negativity associated with bipartitions and also pairs of arbitrary subsystems. As illustration, we consider different types of contiguous and noncontiguous blocks in two dimensional lattices. Exact asymptotic expressions are provided for both first neighbor and full range couplings, which lead in the first case to area laws depending on the orientation and separation of the blocks.