10,417 research outputs found
Entanglement of a 3D generalization of the Kitaev model on the diamond lattice
We study the entanglement properties of a three dimensional generalization of
the Kitaev honeycomb model proposed by Ryu [Phys. Rev. B 79, 075124, (2009)].
The entanglement entropy in this model separates into a contribution from a
gauge field and that of a system of hopping Majorana fermions, similar to
what occurs in the Kitaev model. This separation enables the systematic study
of the entanglement of this 3D interacting bosonic model by using the tools of
non-interacting fermions. In this way, we find that the topological
entanglement entropy comes exclusively from the gauge field, and that it
is the same for all of the phases of the system. There are differences,
however, in the entanglement spectrum of the Majorana fermions that distinguish
between the topologically distinct phases of the model. We further point out
that the effect of introducing vortex lines in the gauge field will only
change the entanglement contribution of the Majorana fermions. We evaluate this
contribution to the entanglement which arises due to gapless Majorana modes
that are trapped by the vortex lines.Comment: 25 pages, 5 figures. Invited article to JSTAT Special Issue: Quantum
Entanglement in Condensed Matter Physic
Absence of topological insulator phases in non-Hermitian PT-symmetric Hamiltonians
In this work we consider a generalization of the symmetry classification of
topological insulators to non-Hermitian Hamiltonians which satisfy a combined
-symmetry (parity and time-reversal). We show via examples, and explicit
bulk and boundary state proofs that the typical paradigm of forming topological
insulator states from Dirac Hamiltonians is not compatible with the
construction of non-Hermitian -symmetric Hamiltonians. The topological
insulator states are -breaking phases and have energy spectra which are
complex (not real) and thus such non-Hermitian Hamiltonians are not consistent
quantum theories.Comment: 5 pages, 1 figur
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