Phase transitions in the Haldane-Hubbard model with ionic potentials

TL;DR

This study uses exact diagonalization to map the phase diagram of the Haldane-Hubbard model with ionic potentials, revealing various insulator and Chern insulator phases and characterizing their phase transitions.

Contribution

It provides a detailed analysis of phase transitions in the Haldane-Hubbard model, including the continuous deformation of Chern insulator phases without gap closure.

Findings

C=1 phase can be deformed into C=2 phase without gap closure under periodic boundary conditions.

Phase transitions between different phases are mostly first-order, except for a continuous transition between C=1 and C=2 phases.

Gap closure occurs at phase boundaries under twisted boundary conditions, indicating topological phase transitions.

Abstract

By employing the exact-diagonalization method, we revisit the ground-state phase diagram of the Haldane-Hubbard model on the honeycomb lattice with staggered sublattice potentials. The phase diagram includes the band insulator, Mott insulator, and two Chern insulator phases with Chern numbers C=2 and C=1, respectively. The character of transitions between different phases is studied by analyzing the lower-lying energy levels, excitation gaps, structure factors, and fidelity metric. We find that the C=1 phase can be continuously deformed into the C=2 phase without a gap closure in the periodic boundary condition, while a further analysis on the Berry curvatures indicates that the excitation gap closes at the phase boundary in a twisted boundary condition, accompanied by the discontinuities of structure factors. All the other phase transitions are found to be first-order ones as expected.