Interacting spin-1 bosons in a two-dimensional optical lattice

TL;DR

This paper investigates the ground state phases of spin-1 bosons in a 2D optical lattice using quantum Monte Carlo simulations, revealing magnetic orderings and phase transition characteristics.

Contribution

It provides the first detailed phase diagram of spin-1 bosons in 2D optical lattices, highlighting magnetic properties and the nature of phase transitions for different interaction types.

Findings

Ferromagnetic interactions lead to a fully ferromagnetic phase.

Antiferromagnetic interactions induce spin nematic order in odd Mott lobes.

The superfluid-insulator transition varies between first and second order depending on density.

Abstract

We study, using quantum Monte Carlo (QMC) simulations, the ground state properties of spin-1 bosons trapped in a square optical lattice. The phase diagram is characterized by the mobility of the particles (Mott insulating or superfluid phase) and by their magnetic properties. For ferromagnetic on-site interactions, the whole phase diagram is ferromagnetic and the Mott insulators-superfluid phase transitions are second order. For antiferromagnetic on-site interactions, spin nematic order is found in the odd Mott lobes and in the superfluid phase. Furthermore, the superfluid-insulator phase transition is first or second order depending on whether the density in the Mott is even or odd. Inside the even Mott lobes, we observe a singlet-to-nematic transition for certain values of the interactions. This transition appears to be first order.