Competing exotic quantum phases of spin-$1/2$ ultra-cold lattice bosons with extended spin interactions

TL;DR

This paper explores the complex ground state phases of a two-component spin-1/2 Bose gas in optical lattices, revealing a variety of magnetic and superfluid phases through theoretical and computational methods.

Contribution

It introduces a comprehensive phase diagram for spinor Bose gases with spin interactions, including interconversion effects, using mean-field and quantum Monte Carlo techniques.

Findings

Identification of antiferromagnetic Mott insulators

Discovery of ferromagnetic and antiferromagnetic superfluids

Mapping of the phase diagram with spin interactions

Abstract

Advances in pure optical trapping techniques now allow the creation of degenerate Bose gases with internal degrees of freedom. Systems such as ${}^{87}$Rb, $^{39}$K or ${}^{23}$Na in the $F=1$ hyperfine state offer an ideal platform for studying the interplay of superfluidity and quantum magnetism. Motivated by the experimental developments, we study ground state phases of a two-component Bose gas loaded on an optical lattice. The system is described effectively by the Bose-Hubbard Hamiltonian with onsite and near neighbor spin-spin interactions. An important feature of our investigation is the inclusion of interconversion (spin flip) terms between the two species, which has been observed in optical lattice experiments. Using mean-field theory and quantum Monte Carlo simulations, we map out the phase diagram of the system. A rich variety of phases is identified, including antiferromagnetic (AF) Mott insulators, ferromagnetic and AF superfluids.