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arXiv:1203.2928 · Physical Review B

Fluctuation-induced topological quantum phase transitions in quantum spin-Hall and anomalous-Hall insulators

Jan Carl Budich, Ronny Thomale, Gang Li, Manuel Laubach, Shoucheng Zhang

Published Nov 16, 2012• 78 citations
arXivHTMLPDF

Abstract

We investigate the role of quantum fluctuations in topological quantum phase transitions of quantum spin-Hall insulators and quantum anomalous-Hall insulators. Employing the variational cluster approximation to obtain the single-particle Green's function of the interacting many-body system, we characterize different phases by direct calculation of the recently proposed topological order parameter for interacting systems. We pinpoint the influence of quantum fluctuations on the quantum spin Hall to Mott insulator transition in several models. Furthermore, we propose a general mechanism by which a topological quantum phase transition can be driven by the divergence of the self-energy induced by interactions.

DOI
10.1103/physrevb.86.201407

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In this thesis, we study the interplay between different topological phases, including both symmetry-protected and topologically ordered states, and how they respond to interaction as well as fluctuations in different proximitized quantum phases. First, it is demonstrated how spinful Majorana edge modes in the presence of charging effects give rise to a novel Kondo effect when coupled to metallic leads. This is followed up by a study on phases of parafermions in fractional quantum (anomalous) Hall - superconductor heterostructures. Finally, it is investigated how the coupling of a Chern insulator to the topologically ordered Toric Code realizes topological Green's function zeros and how they can be used to classify interacting topological systems.
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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.
Transformations between the plateau states of the quantum Hall effect (QHE) are an archetypical example of quantum phase transitions (QPTs) between phases with non-trivial topological order. These transitions appear to be well-described by the single-particle network theories. The long-standing problem with this approach is that it does not account for Coulomb interactions. In this paper, we show that experimental data in the quantum critical regime for both integer and fractional QHEs can be quantitatively explained by the recently developed phenomenological model of QPTs in interacting systems. This model assumes that all effects of interactions are contained in the life-time of fluctuations as set by the Planckian time τP=ℏ/kBTτ_P=\hbar/k_BTτP​=ℏ/kB​T. The dephasing length is taken as the distance traveled by a non-interacting particle along the bulk edge state over this time. We show that the model also provides quantitative description of QPTs between the ground states of anomalous QHE and axion and Chern insulators. These analyzed systems are connected in that the QPTs occur via quantum percolation. Combining the presented results with the results of two companion papers, we conclude that the Planckian time is the encompassing characteristic of QPTs in interacting systems, independent of dimensionality and microscopic physics.