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arXiv:1807.11247

The Haldane model under quenched disorder

Miguel Gonçalves, Pedro Ribeiro, Eduardo V. Castro

Published Jul 30, 2018• 3 citations
arXivHTMLPDF

Abstract

We study the half-filled Haldane model with Anderson and binary disorder and determine its phase diagram, as a function of the Haldane flux and staggered sub-lattice potential, for increasing disorder strength. We establish that disorder stabilizes topologically nontrivial phases in regions of the phase diagram where the clean limit is topologically trivial. At small disorder strength, our results agree with analytical predictions obtained using a first order self-consistent Born approximation, and extend to the intermediate and large disorder values where this perturbative approach fails. We further characterize the phases according to their gapless or gapped nature by determining the spectral weight at the Fermi level. We find that gapless topological nontrivial phases are supported for both Anderson and binary disorder. In the binary case, we find a reentrant topological phase where, starting from a trivial region, a topological transition occurs for increasing staggered potential $η$, followed by a second topological transition to the trivial phase for higher values of $η$.

DOI
10.48550/arxiv.1807.11247

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We study the topological properties of a one-dimensional quasiperiodic-potential-modulated mosaic trimer lattice. To begin with, we first investigate the topological properties of the model in the clean limit free of quasiperiodic disorder based on analytical derivation and numerical calculations of the Zak phase ZZZ and the polarization PPP. Two nontrivial topological phases corresponding to the 1/31/31/3 filling and 2/32/32/3 filling, respectively, are revealed. Then we incorporate the mosaic modulation and investigate the influence of quasiperiodic disorder on the two existing topological phases. Interestingly, it turns out that quasiperiodic disorder gives rise to multiple distinct effects for different fillings. At 2/32/32/3 filling, the topological phase is significantly enhanced by the quasiperiodic disorder and topological Anderson insulator emerges. Based on the calculations of polarization and energy gap, we explicitly present corresponding topological phase diagram in the λ−Jλ-Jλ−J plane. While for the 1/31/31/3 filling case, % the topological phase is dramatically suppressed by the same quasiperiodic disorder. the quasiperiodic disorder dramatically compresses the topological phase, and strikingly, further induces the emergence of reentrant topological phase transitions instead. Furthermore, we verify the topological phase diagrams by computing the many-body ground state fidelity susceptibility for both the 1/31/31/3 filling and 2/32/32/3 filling cases. Our work exemplifies the diverse roles of quasiperiodic disorder in the modulation of topological properties, and will further inspire more research on the competitive and cooperative interplay between topological properties and quasiperiodic disorder.
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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.