5,817 research outputs found
On the classification of Quantum Spin Hall Models
We propose an alternative formulation of the 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the topological arguments including material previously cited as unpublished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
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 -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
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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