Magnetic and Superfluid Transitions in the d=1 Spin-1 Boson Hubbard Model

TL;DR

This study uses Quantum Monte Carlo simulations to explore magnetic and superfluid phase transitions in the one-dimensional spin-1 boson Hubbard model, revealing order-dependent transitions and the existence of a ferromagnetic superfluid phase.

Contribution

It provides the first exact numerical evidence of order-dependent superfluid-insulator transitions in the spin-1 BHM and compares these results with perturbation theory.

Findings

Superfluid-insulator transition is first order for even Mott lobes and second order for odd lobes with antiferromagnetic interactions.

Transitions are continuous in the ferromagnetic case.

Existence of a ferromagnetic superfluid phase in the attractive spin interaction regime.

Abstract

The interplay between magnetism and metal-insulator transitions is fundamental to the rich physics of the single band fermion Hubbard model (FHM). Recent progress in experiments on trapped ultra-cold atoms have made possible the exploration of similar effects in the boson Hubbard model (BHM). This paper reports Quantum Monte Carlo (QMC) simulations of the spin-1 BHM in the ground state. In the case of antiferromagnetic interactions, which favor singlet formation within the Mott insulator lobes, we present exact numerical evidence that the superfluid-insulator phase transition is first (second) order depending on whether the Mott lobe is even (odd). In the ferromagnetic case, the transitions are all continuous. We obtain the phase diagram in the case of attractive spin interactions and demonstrate the existence of the ferromagnetic superfluid. We also compare the QMC phase diagram with a third order perturbation calculation.