Generalized mean field description of entanglement in dimerized spin systems

TL;DR

This paper introduces a generalized mean field approach to analyze entanglement in dimerized spin systems, capturing complex ground state features and phase transitions more accurately than traditional methods.

Contribution

It develops an analytic, pair-based mean field method that improves entanglement and phase diagram predictions in dimerized spin chains, including symmetry restoration techniques.

Findings

Accurately predicts ground state phases and parity breaking.

Captures entanglement properties and their peaks in phase transitions.

Matches well with exact results for finite systems.

Abstract

We discuss a generalized self-consistent mean field (MF) treatment, based on the selection of an arbitrary subset of operators for representing the system density matrix, and its application to the problem of entanglement evaluation in composite quantum systems. As a specific example, we examine in detail a pair MF approach to the ground state (GS) of dimerized spin 1/2 systems with anisotropic ferromagnetic-type XY and XYZ couplings in a transverse field, including chains and arrays with first neighbor and also longer range couplings. The approach is fully analytic and able to capture the main features of the GS of these systems, in contrast with the conventional single spin MF. Its phase diagram differs significantly from that of the latter, exhibiting (Sz) parity breaking just in a finite field window if the coupling between pairs is sufficiently weak, together with a fully dimerized phase below this window and a partially aligned phase above it. It is then shown that through symmetry restoration, the approach is able to correctly predict not only the concurrence of a pair, but also its entanglement with the rest of the chain, which shows a pronounced peak in the parity breaking window. Perturbative corrections allow to reproduce more subtle observables like the entanglement between weakly coupled spins and the low lying energy spectrum. All predictions are tested against exact results for finite systems.