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arXiv:2401.01402 · Physical review. B./Physical review. B

Topological phase transition without single particle gap closing in strongly correlated systems

Peizhi Mai, Jinchao Zhao, Thomas Maier, Barry Bradlyn, Philip Phillips

Published Aug 5, 2024• 10 citations
arXivHTMLPDF

Abstract

We show here two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.

DOI
10.1103/physrevb.110.075105

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•Dec 16, 2015•2 citations
We show here two models where changing topology does not necessarily close the bulk insulating charge gap as demanded in the standard noninteracting picture. From extensive determinantal and dynamical cluster quantum Monte Carlo simulations of the half-filled and quarter-filled Kane-Mele-Hubbard model, we show that, for sufficiently strong interactions at either half- or quarter-filling, a transition between topological and trivial insulators occurs without the closing of a charge gap. To shed light on this behavior, we illustrate that an exactly solvable model reveals that while the single-particle gap remains, the many-body gap does, in fact, close. These two gaps are the same in the noninteracting system but depart from each other as the interaction turns on. We purport that for interacting systems, the proper probe of topological phase transitions is the closing of the many-body rather than the single-particle gap.
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.
It is expected that the interplay between nontrivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo simulations, we provide a concrete example of the Kane-Mele-Hubbard model on an AA-stacking bilayer honeycomb lattice with interlayer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin Hall insulator (QSH), an xy-planexy\text{-plane}xy-plane antiferromagnetic Mott insulator, and an interlayer dimer-singlet insulator. Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the interlayer antiferromagnetic interaction, is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean-field analog and it can be viewed as a transition between bosonic symmetry-protected topological (SPT) states. At one special point, this transition is described by a (2+1)dO(4)(2+1)d\phantom{\rule{4pt}{0ex}}O(4)(2+1)dO(4) nonlinear sigma model with exact SO(4)SO(4)SO(4) symmetry and a topological term at exactly $\mathrm{\ensuremath{\Theta}}=\ensuremath{\pi}$. The relevance of this work towards more general interacting SPT states is discussed.
We prove that the Kane-Mele-Hubbard model with purely imaginary next-nearest-neighbor hoppings has a particle-hole symmetry at half filling. Such a symmetry has interesting consequences including the absence of charge and spin currents along open edges, and the absence of the sign problem in the determinant quantum Monte Carlo simulations. Consequentially, the interplay between band topology and strong correlations can be studied at high numeric precisions. The process that the topological band insulator evolves into the antiferromagnetic Mott insulator as interaction strength increases is studied by calculating both the bulk and edge electronic properties.
We study the interplay between topological and conventional long range order of attractive fermions in a time reversal symmetric Hofstadter lattice using quantum Monte Carlo simulations, focussing on the case of one-third flux quantum per plaquette. At half-filling, the system is unstable towards s-wave pairing and charge-density-wave order at infinitesimally small interactions. At one-third-filling, the noninteracting system is a topological insulator, and a nonzero critical interaction strength is needed to drive a transition from the quantum spin Hall insulator to a superfluid. We probe the topological signature of the phase transition by threading a magnetic flux through a cylinder and observe quantized topological charge pumping.
We study the interplay between topological and conventional long-range order of attractive fermions in a time-reversal-symmetric Hofstadter lattice using quantum Monte Carlo simulations, focusing on the case of one-third flux quantum per plaquette. At half filling, the system is unstable towards sss-wave pairing and charge-density-wave order at infinitesimally small interactions. At one-third filling, the noninteracting system is a topological insulator, and a nonzero critical interaction strength is needed to drive a transition from the quantum spin Hall insulator to a superfluid. We probe the topological signature of the phase transition by threading a magnetic flux through a cylinder and observe quantized topological charge pumping.
Topological phase transitions and the phase diagram of Haldane-Hubbard model are investigated using the variational cluster approach. With increasing the interaction strength, there are two successive topological phase transitions. The first is characterized by the closing and reopening of the single particle gap with the Chern number changing its sign, while the second is featured by the divergence of the topological Hamiltonian's spectrum with the Chern number changing from a non-zero integer to zero. The second topological phase transition is not accompanied with the single particle gap closing but is associated with the zeros of the single particle Green's function. Between these two topological phase transitions, there exists a non-magnetic topological Mott insulating phase with no gapless single particle edge states which cannot be adiabatically connected to any non-interacting Chern insulator.