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Início
Agenda |
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- 22 de janeiro de 2014
16h
Sala Celeste
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Luiz Henrique Bravo dos
Santos
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Perimeter Institute,
Waterloo, Canadá
Aharonov-Bohm
effect in symmetry protected states
Symmetry
protected topological (SPT) states are generalizations of
topological band insulators to interacting systems. They possess
a gapped bulk spectrum together with symmetry protected edge
states, with no topological order. There has been recently an
intense effort to classify SPT states both in terms of group
cohomology as well as from the point of view of effective field
theories. An interesting related question is to understand the
structute of lattice models that realize SPT physics. In this
talk, I shall present a class of lattice models describing the
egde of non-chiral two-dimensional bosonic SPT states protected
by Z_N symmetry. A crucial aspect of the construction relies on
finding the correct non-trivial Z_N symmetry realizations on the
edge consistent with all the possible classes of SPT states.
Then I shall discuss the Aharonov-Bohm effect on the many-body
SPT state by studying this many-body effect on the
aforementioned gapless edge states. The effect of a Z_N gauge
flux on the egde states is formulated in terms of twisted
boundary conditions of the lattice models. The low energy
spectral shifts due to the gauge flux are shown to depend on
each of the SPT classes in a predictable way. I shall, in the
course of this talk, present numerical results of exact
diagonalization of our lattice Hamiltonians that support this
analysis. This work is done in collaboration with Juven Wang and
appears in arXiv:1310.8291. -
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