5,817 research outputs found

    On the Z2Z_2 classification of Quantum Spin Hall Models

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    We propose an alternative formulation of the Z2Z_2 topological index for quantum spin Hall systems and band insulators when time reversal invariance is not broken. The index is expressed in terms of the Chern numbers of the bands of the model, and a connection with the number of pairs of robust edge states is thus established. The alternative index is easy to compute in most cases of interest. We also discuss connections with the recently proposed spin Chern number for quantum spin Hall models.Comment: Presentation changed to improve clarity, some technical aspects of the topological arguments including material previously cited as unpublished notes have now been added as an appendi

    Disorder-driven destruction of a non-Fermi liquid semimetal via renormalization group

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    We investigate the interplay of Coulomb interactions and short-range-correlated disorder in three dimensional systems where absent disorder the non-interacting band structure hosts a quadratic band crossing. Though the clean Coulomb problem is believed to host a 'non-Fermi liquid' phase, disorder and Coulomb interactions have the same scaling dimension in a renormalization group (RG) sense, and thus should be treated on an equal footing. We therefore implement a controlled ϵ\epsilon-expansion and apply it at leading order to derive RG flow equations valid when disorder and interactions are both weak. We find that the non-Fermi liquid fixed point is unstable to disorder, and demonstrate that the problem inevitably flows to strong coupling, outside the regime of applicability of the perturbative RG. An examination of the flow to strong coupling suggests that disorder is asymptotically more important than interactions, so that the low energy behavior of the system can be described by a non-interacting sigma model in the appropriate symmetry class (which depends on whether exact particle-hole symmetry is imposed on the problem). We close with a discussion of general principles unveiled by our analysis that dictate the interplay of disorder and Coulomb interactions in gapless semiconductors, and of connections to many-body localized systems with long-range interactions.Comment: 15 pages, 4 figure

    Many body localization with long range interactions

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    Many body localization (MBL) has emerged as a powerful paradigm for understanding non-equilibrium quantum dynamics. Folklore based on perturbative arguments holds that MBL only arises in systems with short range interactions. Here we advance non-perturbative arguments indicating that MBL can arise in systems with long range (Coulomb) interactions. In particular, we show using bosonization that MBL can arise in one dimensional systems with ~ r interactions, a problem that exhibits charge confinement. We also argue that (through the Anderson-Higgs mechanism) MBL can arise in two dimensional systems with log r interactions, and speculate that our arguments may even extend to three dimensional systems with 1/r interactions. Our arguments are `asymptotic' (i.e. valid up to rare region corrections), yet they open the door to investigation of MBL physics in a wide array of long range interacting systems where such physics was previously believed not to arise.Comment: Expanded discussion of higher dimensions, updated reference
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