Competing Chiral Orders in the Topological Haldane-Hubbard Model of Spin-1/2 Fermions and Bosons

TL;DR

This paper explores the rich magnetic phases and chiral spin liquids in the strongly correlated Haldane-Hubbard model for ultracold atoms, revealing diverse chiral orders and their thermal behaviors.

Contribution

It introduces a comprehensive analysis of competing chiral magnetic orders and spin liquids in the Haldane-Hubbard model using mean field and classical spin Hamiltonian approaches.

Findings

Identification of various chiral magnetic orders including tetrahedral, cone, and spiral states.

Discovery of thermal fluctuation effects leading to crossovers and phase transitions.

Discussion of experimental implications for cold atom realizations.

Abstract

Motivated by experiments on ultracold atoms which have realized the Haldane model for a Chern insulator, we consider its strongly correlated Mott limit with spin-$1/2$ fermions. We find that slave rotor mean field theory yields gapped or gapless chiral spin liquid Mott insulators. To study competing magnetic orders, we consider the strong coupling effective spin Hamiltonian which includes chiral three-spin exchange. We obtain its classical phase diagram, uncovering various chiral magnetic orders including tetrahedral, cone, and noncoplanar spiral states which can compete with putative chiral quantum spin liquids. We study the effect of thermal fluctuations on these states, identifying crossovers in the spin chirality, and phase transitions associated with lattice symmetry breaking. We also discuss analogous effective spin Hamiltonians for correlated spin-$1/2$ bosons. Finally, we point out possible experimental implications of our results for cold atom experiments.