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arXiv:2107.10056 · Physical review. B./Physical review. B

Interplay of interactions, disorder, and topology in the Haldane-Hubbard model

Tian-Cheng Yi, Shijie Hu, Eduardo V. Castro, Rubem Mondaini

Published Nov 10, 2021• 23 citations
arXivHTMLPDF

Abstract

We investigate the ground-state phase diagram of the spinless Haldane-Hubbard model in the presence of quenched disorder, contrasting results obtained from both exact diagonalization and the density matrix renormalization group, applied to a honeycomb cylinder. The interplay of disorder, interactions, and topology gives rise to a rich phase diagram and, in particular, highlights the possibility of a disorder-driven trivial-to-topological transition in the presence of finite interactions. That is, the topological Anderson insulator, demonstrated in noninteracting settings, is shown to be stable in the presence of sufficiently small interactions before a charge density wave Mott insulator sets in. We further promote a finite-size analysis of the transition to the ordered state in the presence of disorder, finding a mixed character of first- and second-order transitions in finite lattices, tied to the specific conditions of disorder realizations and boundary conditions used.

DOI
10.1103/physrevb.104.195117

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We examine the emergence of topological Anderson insulating phases in the spinful Haldane model with Hubbard and next-neighbor density-density interactions, subject to Anderson disorder. Using finite-size exact diagonalization, we characterize the phases that arise from the interplay between topology, interactions, and disorder. In addition to standard C=2C=2C=2 topological Anderson phases, we observe an antiferromagnetic C=1C=1C=1 topological Anderson phase, consistent with the antiferromagnetic quantum anomalous Hall insulator previously identified in the clean model at finite staggered mass. We further analyze these phases using a neural network trained on the exact diagonalization data. Our results support the hypothesis that an explicit charge imbalance is required to induce the C=1C=1C=1 phase, generated by Anderson disorder rather than by a staggered mass.
We investigate the phase diagram of spinless fermions with nearest- and next-nearest-neighbor density-density interactions on the honeycomb lattice at half-filling. Using exact diagonalization techniques of the full Hamiltonian and constrained subspaces, combined with a careful choice of finite-size clusters, we determine the different charge orderings that occur for large interactions. In this regime, we find a two-sublattice N\'eel-like state, a charge modulated state with a tripling of the unit cell, a zigzag phase, and a charge ordered state with a 12-site unit cell we call N\'eel domain wall crystal, as well as a region of phase separation for attractive interactions. A sizable region of the phase diagram is classically degenerate, but it remains unclear whether an order-by-disorder mechanism will lift the degeneracy. For intermediate repulsion, we find evidence for a Kekul\'e or plaquette bond-order wave phase. We also investigate the possibility of a spontaneous Chern insulator phase (dubbed topological Mott insulator), as previously put forward by several mean-field studies. Although we are unable to detect convincing evidence for this phase based on energy spectra and order parameters, we find an enhancement of current-current correlations with the expected spatial structure compared to the noninteracting situation. While for the studied $t\ensuremath{-}{V}_{1}\ensuremath{-}{V}_{2}$ model, the phase transition to the putative topological Mott insulator is preempted by the phase transitions to the various ordered states, our findings might hint at the possibility for a topological Mott insulator in an enlarged Hamiltonian parameter space, where the competing phases are suppressed.
We investigate the quantum many-body instabilities of the extended Hubbard model for spinless fermions on the honeycomb lattice with repulsive nearest-neighbor and second-nearest-neighbor density-density interactions. Recent exact diagonalization and infinite density matrix renormalization group results suggest that a putative topological Mott insulator phase driven by the second-nearest-neighbor repulsion is suppressed, while other numerically exact approaches support the topological Mott insulator scenario. In the present work, we employ the functional renormalization group (fRG) for correlated fermionic systems. Our fRG results hint at a strong suppression of the scattering processes stabilizing the topological Mott insulator. From analyzing the effects of fermionic fluctuations, we obtain a phase diagram, which is the result of the competition of various charge ordering instabilities.
We analyze the influence of disorder and strong correlations on the topology of two-dimensional Chern insulators. A mean-field calculation in the half-filled Haldane model with extended Hubbard interactions and Anderson disorder shows that the disorder favors topology in the interacting case and extends the topological phase to a larger region of the Hubbard parameters. In the absence of a staggered potential, we find a novel disorder-driven topological phase with Chern number C=1C=1C=1, with the coexistence of topology with long-range spin and charge orders. More conventional topological Anderson insulating phases are also found in the presence of a finite staggered potential.