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arXiv:2207.01638 · Physical Review Research

Topological Mott insulator at quarter filling in the interacting Haldane model

Peizhi Mai, Benjamin E. Feldman, Philip Phillips

Published Mar 3, 2023• 59 citations
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Abstract

While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically nontrivial Haldane model, we show that a quarter-filled state emerges with a nonzero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: Analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid-state systems are discussed.

DOI
10.1103/physrevresearch.5.013162

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While the recent advances in topology have led to a classification scheme for electronic bands described by the standard theory of metals, a similar scheme has not emerged for strongly correlated systems such as Mott insulators in which a partially filled band carries no current. By including interactions in the topologically nontrivial Haldane model, we show that a quarter-filled state emerges with a nonzero Chern number provided the interactions are sufficiently large. We first motivate this result on physical grounds and then by two methods: Analytically by solving exactly a model in which interactions are local in momentum space and then numerically through the corresponding Hubbard model. All methods yield the same result: For sufficiently large interaction strengths, the quarter-filled Haldane model is a ferromagnetic topological Mott insulator with a Chern number of unity. Possible experimental realizations in cold-atom and solid-state systems are discussed.
By means of exact diagonalizations, the Bernevig-Hughes-Zhang model at quarter-filling in the limit of strong Hubbard on-site repulsion is investigated. We find that the noninteracting metallic state will be turned into a Chern insulator with saturated magnetization under strong correlations. That is, at such a metal-insulator transition, both the topological and the magnetic properties of the system are changed due to spontaneous breaking of time-reversal symmetry in the ground states. According to our findings, this topological phase transition seems to be of first order. Our results illustrate the interesting physics in topological Mott transitions and provide guidance to the search of more interaction-induced topological phases in similar systems.
In non-interacting systems, bands from non-trivial topology emerge strictly at half-filling and exhibit either the quantum anomalous Hall or spin Hall effects. Here we show using determinantal quantum Monte Carlo and an exactly solvable strongly interacting model that these topological states now shift to quarter filling. A topological Mott insulator is the underlying cause. The peak in the spin susceptibility is consistent with a possible ferromagnetic state at T = 0. The onset of such magnetism would convert the quantum spin Hall to a quantum anomalous Hall effect. While such a symmetry-broken phase typically is accompanied by a gap, we find that the interaction strength must exceed a critical value for this to occur. Hence, we predict that topology can obtain in a gapless phase but only in the presence of interactions in dispersive bands. These results explain the recent quarter-filled quantum anomalous Hall effects seen in moiré systems.
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We investigate the emergence of topological features in the charge excitations of Mott insulators in the Chern-Hubbard model. In the strong correlation regime, treating electrons as the sum of holons and doublons excitations, we compute the topological phase diagram of Mott insulators at half-filling using composite operator formalism. The Green function zeros manifest as the tightly bound pairs of such elementary excitations of the Mott insulators. Our analysis examines the winding number associated with the occupied Hubbard bands and the band of Green's function zeros. We show that both the poles and zeros show gapless states and zeros, respectively, in line with bulk-boundary correspondence. The gapless edge states emerge in a junction geometry connecting a topological Mott band insulator and a topological Mott zeros phase. These include an edge electronic state that carries a charge and a charge-neutral gapless zero mode. Our study is relevant to several twisted materials with flat bands where interactions play a dominant role.
We study the topological properties of an extended Bose-Hubbard model with cyclically modulated hopping and on-site potential parameters, which can be realized with ultracold bosonic atoms in a one-dimensional optical superlattice. We show that the interacting bosonic chain at half filling and in the deep Mott insulating regime can simulate bosonic Chern insulators with a topological phase diagram similar to that of the Haldane model of noninteracting fermions. Furthermore, we explore the topological properties of the ground state by calculating the many-body Chern number, the quasiparticle energy spectrum with gapless edge modes, the topological pumping of the interacting bosons, and the topological phase transition from normal (trivial) to topological Mott insulators. We also present the global phase diagram of the many-body ground state, which contains a superfluid phase and two Mott insulating phases with trivial (a zero Chern number) and nontrivial topologies (a nonzero Chern number), respectively.
Abstract Magic-angle twisted bilayer graphene has recently become a thriving material platform realizing correlated electron phenomena taking place within its topological flat bands. Several numerical and analytical methods have been applied to understand the correlated phases therein, revealing some similarity with the quantum Hall physics. In this work, we provide a Mott-Hubbard perspective for the TBG system. Employing the large-scale density matrix renormalization group on the lattice model containing the projected Coulomb interactions only, we identify a first-order quantum phase transition between the insulating stripe phase and the quantum anomalous Hall state with the Chern number of ±1. Our results not only shed light on the mechanism of the quantum anomalous Hall state discovered at three-quarters filling, but also provide an example of the topological Mott insulator, i.e., the quantum anomalous Hall state in the strong coupling limit.