Hierarchical Mean-Field Theories

TL;DR

Hierarchical mean-field theory (HMFT) is introduced as a systematic approach for analyzing strongly coupled many-particle systems, effectively handling competing orders and phases, with applications demonstrated in optical lattice systems.

Contribution

The paper introduces HMFT, a new group-theoretic mean-field approach for studying complex systems with competing interactions and phases.

Findings

HMFT provides reliable predictions for phase behavior.

Applicable to optical lattice systems with competing orders.

Simplifies analysis of non-linear couplings in many-particle systems.

Abstract

We present a systematic and reliable methodology, termed hierarchical mean-field theory (HMFT), to study and predict the behavior of strongly coupled many-particle systems. HMFT is a simple approximation, based upon group theoretical grounds, which deals with competing orders on an equal footing. It is distinctly suitable when the various phases displayed by a system are the result of competing interactions and non-linear couplings of their constituents matter fields. We show applications relevant for systems implemented in optical lattices.