Entanglement Mean Field Theory and the Curie-Weiss Law

TL;DR

This paper introduces an entanglement mean field theory (EMFT) to analyze two-body properties in many-body systems, predicting phase behavior and critical exponents, including the Curie-Weiss law for correlations.

Contribution

The paper develops EMFT as a novel approach to study two-body properties and phase transitions in quantum and classical many-body systems.

Findings

Predicted phase diagrams for XY, XX, and Heisenberg models.

Calculated critical exponents within EMFT.

Derived the Curie-Weiss law for correlations in the Heisenberg model.

Abstract

The mean field theory, in its different hues, form one of the most useful tools for calculating the single-body physical properties of a many-body system. It provides important information, like critical exponents, of the systems that do not yield to an exact analytical treatment. Here we propose an entanglement mean field theory (EMFT) to obtain the behavior of the two-body physical properties of such systems. We apply this theory to predict the phases in paradigmatic strongly correlated systems, viz. the transverse anisotropic XY, the transverse XX, and the Heisenberg models. We find the critical exponents of different physical quantities in the EMFT limit, and in the case of the Heisenberg model, we obtain the Curie-Weiss law for correlations. While the exemplary models have all been chosen to be quantum ones, classical many-body models also render themselves to such a treatment, at the level of correlations.