SciPost Phys. 11, 003 (2021) ·
published 9 July 2021

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Usually duality process keeps energy spectrum invariant. In this paper, we provide a duality, which keeps entanglement spectrum invariant, in order to diagnose quantum entanglement of nonHermitian noninteracting fermionic systems. We limit our attention to nonHermitian systems with a complete set of biorthonormal eigenvectors and an entirely real energy spectrum.
The original system has a reduced density matrix $\rho_\mathrm{o}$ and the real space is partitioned via a projecting operator $\mathcal{R}_{\mathrm o}$. After dualization, we obtain a
new reduced density matrix $\rho_{\mathrm{d}}$ and a new real space projector $\mathcal{R}_{\mathrm d}$. Remarkably, entanglement spectrum and entanglement entropy keep invariant. Inspired by the duality, we
defined two types of nonHermitian models, upon $\mathcal R_{\mathrm{o}}$ is given.
In typeI exemplified by the ``nonreciprocal model'', there exists
at least one duality such that $\rho_{\mathrm{d}}$ is Hermitian. In other
words, entanglement information of typeI nonHermitian models with a given $\mathcal{R}_{\mathrm{o}}$ is entirely controlled by Hermitian models
with $\mathcal{R}_{\mathrm{d}}$. As a result, we are
allowed to apply known results of Hermitian systems to efficiently obtain
entanglement properties of typeI models. On the other hand,
the duals of typeII models, exemplified by ``nonHermitian
SuSchriefferHeeger model'', are always nonHermitian. For the practical purpose, the
duality provides a potentially \textit{efficient} computation route to entanglement of
nonHermitian systems. Via connecting different models, the duality also sheds lights on either trivial or nontrivial role of
nonHermiticity played in quantum entanglement, paving the way to potentially systematic
classification and characterization of nonHermitian systems from the
entanglement perspective.
Prof. Ye: "Dear Referee, We would like..."
in Submissions  report on Entanglement, NonHermiticity, and Duality