Non-Hermitian skin effect as an impurity problem
- URL: http://arxiv.org/abs/2105.01197v1
- Date: Mon, 3 May 2021 22:32:04 GMT
- Title: Non-Hermitian skin effect as an impurity problem
- Authors: Federico Roccati
- Abstract summary: A striking feature of non-Hermitian tight-binding Hamiltonians is the high sensitivity of both spectrum and eigenstates to boundary conditions.
Here we devise a general procedure to calculate the eigenstates of non-Hermitian tight-binding Hamiltonians under open boundary conditions.
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- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: A striking feature of non-Hermitian tight-binding Hamiltonians is the high
sensitivity of both spectrum and eigenstates to boundary conditions. Indeed, if
the spectrum under periodic boundary conditions is point gapped, by opening the
lattice the non-Hermitian skin effect will necessarily occur. Finding the exact
skin eigenstates may be demanding in general, and many methods in the
literature are based on ansatzes and on recurrence equations for the
eigenstates' components. Here we devise a general procedure based on the
Green's function method to calculate the eigenstates of non-Hermitian
tight-binding Hamiltonians under open boundary conditions. We apply it to the
Hatano-Nelson and non-Hermitian SSH models and finally we contrast the edge
states localization with that of bulk states.
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