Haldane-Hubbard Mott Insulator: From Tetrahedral Spin Crystal to Chiral Spin Liquid

TL;DR

This paper investigates the phase transitions in the Haldane-Hubbard Mott insulator on a honeycomb lattice, revealing a transition from tetrahedral magnetic order to a chiral spin liquid with semion excitations using advanced numerical methods.

Contribution

It identifies a novel quantum phase transition from tetrahedral spin order to a chiral spin liquid in a honeycomb lattice model, supported by detailed numerical and theoretical analysis.

Findings

Tetrahedral spin order is stabilized without third-neighbor hopping.

Third-neighbor hopping induces a transition to a chiral spin liquid.

Chiral spin liquid exhibits gapped semion excitations.

Abstract

Motivated by cold atom experiments on Chern insulators, we study the honeycomb lattice Haldane-Hubbard Mott insulator of spin-$1/2$ fermions using exact diagonalization and density matrix renormalization group methods. We show that this model exhibits various chiral magnetic orders including a wide regime of triple-Q tetrahedral order. Incorporating third-neighbor hopping frustrates and ultimately melts this tetrahedral spin crystal. From analyzing low energy spectra, many-body Chern numbers, entanglement spectra, and modular matrices, we identify the molten state as a chiral spin liquid (CSL) with gapped semion excitations. We formulate and study the Chern-Simons-Higgs field theory of the exotic CSL-to-tetrahedral spin crystallization transition.