Quantum magnetism of spinor bosons in optical lattices with synthetic non-Abelian gauge fields

TL;DR

This paper investigates quantum magnetism of spinor bosons in optical lattices with non-Abelian gauge fields, revealing new magnetic phases, excitations, and experimental signatures, with potential realizations in current and future experiments.

Contribution

It introduces a Rotated ferromagnetic Heisenberg model derived from spinor bosons with non-Abelian gauge fields, identifying new ground states and excitations, and proposing experimental detection methods.

Findings

Discovery of in-commensurate magnons with tunable gap minima.

Identification of a new spin-orbital entangled ground state.

Prediction of distinct spectral features in Bragg spectroscopy.

Abstract

We study quantum magnetism of interacting spinor bosons at integer fillings hopping in a square lattice in the presence of non-Abelian gauge fields. In the strong coupling limit, it leads to the Rotated ferromagnetic Heisenberg model (RFHM) which is a new class of quantum spin model. We introduce Wilson loops to characterize frustrations and gauge equivalent classes. For a special equivalent class, we identify a new spin-orbital entangled commensurate ground state. It supports not only commensurate magnons, but also a new gapped elementary excitation: in-commensurate magnons with two gap minima continuously tuned by the SOC strength. At low temperatures, these magnons lead to dramatic effects in many physical quantities such as density of states, specific heat, magnetization, uniform susceptibility, staggered susceptibility and various spin correlation functions. The commensurate magnons lead to a pinned central peak in the angle resolved light or atom Bragg spectroscopy. However, the in-commensurate magnons split it into two located at their two gap minima. At high temperatures, the transverse spin structure factors depend on the SOC strength explicitly. The whole set of Wilson loops can be mapped out by measuring the specific heat at the corresponding orders in the high temperature expansion. We argue that one gauge may be realized in current experiments and other gauges may also be realized in near future experiments. The results achieved along the exact solvable line sets up the stage to investigate dramatic effects when tuning away from it by various means. We sketch the crucial roles to be played by these magnons at other equivalent classes, with spin anisotropic interactions and in the presence of finite magnetic fields. Various experimental detections of these new phenomena are discussed. Rotated Anti-ferromagnetic Heisenberg model are also briefly mentioned.