Phase Diagrams for Spin-1 Bosons in an Optical Lattice

TL;DR

This paper maps out the phase diagrams of spin-1 bosons in an optical lattice, revealing how different Zeeman effects influence phase transitions and coexistence at various temperatures.

Contribution

It provides a comprehensive mean-field analysis of phase diagrams considering both linear and quadratic Zeeman effects at zero and finite temperatures.

Findings

Large quadratic Zeeman effect leads to a first-order transition from nematic to ferromagnetic phase.

Small quadratic Zeeman effect results in a nematic to partially magnetic transition, then to ferromagnetic.

Phase coexistence and phase separation occur depending on the quadratic Zeeman effect magnitude.

Abstract

In this paper, the phase diagrams of a polar spin-1 Bose gas in a three-dimensional optical lattice with linear and quadratic Zeeman effects both at zero and finite temperatures are obtained within mean-field theory. The phase diagrams can be regrouped to two different parameter regimes depending on the magnitude of the quadratic Zeeman effect $Q$. For large $Q$, only a first-order phase transition from the nematic (NM) phase to the fully magnetic (FM) phase is found, while in the case of small $Q$, a first-order phase transition from the nematic phase to the partially magnetic (PM) phase, plus a second-order phase transition from the PM phase to the FM phase is obtained. If a net magnetization in the system exists, the first-order phase transition causes a coexistence of two phases and phase separation: for large $Q$, NM and FM phases and for small $Q$, NM and PM phases. The phase diagrams in terms of net magnetization are also obtained.