Evaluation of ground state entanglement in spin systems with the random phase approximation

TL;DR

This paper presents a mean field plus random phase approximation method to evaluate ground state entanglement in spin systems, providing analytic expressions for entanglement measures in large and small systems.

Contribution

It introduces a tractable RPA-based approach for calculating entanglement in spin arrays, including analytic formulas for large systems and parity effects.

Findings

Analytic expressions for entanglement entropy in large arrays.

Exact results for negativity between subsystems in large spin systems.

Effective treatment of parity breaking and restoration effects.

Abstract

We discuss a general treatment based on the mean field plus random phase approximation (RPA) for the evaluation of subsystem entropies and negativities in ground states of spin systems. The approach leads to a tractable general method, becoming straightforward in translationally invariant arrays. The method is examined in arrays of arbitrary spin with $XYZ$ couplings of general range in a uniform transverse field, where the RPA around both the normal and parity breaking mean field state, together with parity restoration effects, are discussed in detail. In the case of a uniformly connected $XYZ$ array of arbitrary size, the method is shown to provide simple analytic expressions for the entanglement entropy of any global bipartition, as well as for the negativity between any two subsystems, which become exact for large spin. The limit case of a spin $s$ pair is also discussed.