Topological phase transitions in the interacting Haldane model
题目：Topological phase transitions in the interacting Haldane model
We investigate the ground-state phase diagram of the spinful extended Haldane-Hubbard model on the honeycomb lattice using an exact-diagonalization (ED), mean-field (MF) approach, and further complement it with the infinite density matrix renormalization group (iDMRG), applied to an infinite honeycomb cylinder. This model, governed by both on-site and nearest-neighbor interactions, can result in two types of insulators with finite local order parameters, either with spin or charge ordering. A third one, a topologically nontrivial insulator with nonlocal order is manifest in ED results. However, this state can not been observed in MF and iDMRG. Our study highlights how finite-size effects may result in misleading conclusions on the coexistence of finite local order parameters and nontrivial topology in this model.
We further 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.
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