SciPost Phys. 7, 069 (2019) ·
published 28 November 2019

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We study the properties of the entanglement spectrum in gapped noninteracting nonHermitian systems, and its relation to the topological properties of the system Hamiltonian. Two different families of entanglement Hamiltonians can be defined in nonHermitian systems, depending on whether we consider only right (or equivalently only left) eigenstates or a combination of both left and right eigenstates. We show that their entanglement spectra can still be computed efficiently, as in the Hermitian limit. We discuss how symmetries of the Hamiltonian map into symmetries of the entanglement spectrum depending on the choice of the manybody state. Through several examples in one and two dimensions, we show that the biorthogonal entanglement Hamiltonian directly inherits the topological properties of the Hamiltonian for line gapped phases, with characteristic singular and energy zero modes. The right (left) density matrix carries distinct information on the topological properties of the manybody right (left) eigenstates themselves. In purely point gapped phases, when the energy bands are not separable, the relation between the entanglement Hamiltonian and the system Hamiltonian breaks down.
SciPost Phys. 6, 060 (2019) ·
published 17 May 2019

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Among the different platforms to engineer Majorana fermions in
onedimensional topological superconductors, topological insulator nanowires
remain a promising option. Threading an odd number of flux quanta through these
wires induces an odd number of surface channels, which can then be gapped with
proximity induced pairing. Because of the flux and depending on energetics, the
phase of this surface pairing may or may not wind around the wire in the form
of a vortex. Here we show that for wires with discrete rotational symmetry,
this vortex is necessary to produce a fully gapped topological superconductor
with localized Majorana end states. Without a vortex the proximitized wire
remains gapless, and it is only if the symmetry is broken by disorder that a
gap develops, which is much smaller than the one obtained with a vortex. These
results are explained with the help of a continuum model and validated
numerically with a tight binding model, and highlight the benefit of a vortex
for reliable use of Majorana fermions in this platform.