Phases and Transitions in the Spin-1 Bose-Hubbard Model: Systematics of a Mean-field Theory

TL;DR

This paper extends mean-field theory to the spin-1 Bose-Hubbard model, revealing complex phase diagrams with various superfluid, Mott insulator, and normal liquid phases, including first- and second-order transitions and tricritical points.

Contribution

It introduces a generalized mean-field approach for the spin-1 Bose-Hubbard model, capturing diverse superfluid phases and complex transition behaviors not seen in the spinless case.

Findings

Identification of polar and ferromagnetic superfluid phases.

Discovery of first-order superfluid-Mott insulator transitions at finite temperature.

Rich phase diagrams with tricritical points and multiple transition types.

Abstract

We generalize the mean-field theory for the spinless Bose-Hubbard model to account for the different types of superfluid phases that can arise in the spin-1 case. In particular, our mean-field theory can distinguish polar and ferromagnetic superfluids, Mott insulators which arise at integer fillings at zero temperature, and normal Bose liquids into which the Mott insulators evolve at finite temperatures. We find, in contrast to the spinless case, that several of the superfluid-Mott insulator transitions are first-order at finite temperatures. Our systematic study yields rich phase diagrams that include, first-order and second-order transitions, and a variety of tricritical points. We discuss the possibility of realizing such phase diagrams in experimental systems.