Abstract
We propose a method of computing and studying entanglement quantities in non-Hermitian systems by use of a biorthogonal basis. We find that the entanglement spectrum characterizes the topological properties in terms of the existence of mid-gap states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model with parity and time-reversal symmetry (PT symmetry) and the non-Hermitian Chern insulators. In addition, we find that at a critical point in the PT symmetric SSH model, the entanglement entropy has a logarithmic scaling with corresponding central charge $c=-2$. This critical point then is a free-fermion lattice realization of the non-unitary conformal field theory.
Highlights
In contemporary condensed matter physics, quantum entanglement plays a pivotal role in characterizing and obtaining a deeper understanding of many-body quantum systems
We found, at a critical point appearing in the non-Hermitian SSH model, the entanglement entropy decreases logarithmically in the subsystem size: this signals the emergence of nonunitary conformal field theory (CFT)
Since it has been known that the existence of the bulk-edge correspondence in non-Hermitian systems is sensitive to boundary conditions, in the following we investigate the entanglement spectrum of the non-Hermitian gapped phases by setting entangling boundary either in the y direction or in the x direction
Summary
In contemporary condensed matter physics, quantum entanglement plays a pivotal role in characterizing and obtaining a deeper understanding of many-body quantum systems. We show that the topological gapped (trivial) PT-symmetric phase in the non-Hermitian SSH model supports (does not support) robust mid-gap states in the entanglement spectrum. We found, at a critical point appearing in the non-Hermitian SSH model, the entanglement entropy decreases logarithmically in the subsystem size: this signals the emergence of nonunitary conformal field theory (CFT). At the critical point separating the trivial PT-symmetric phase and the spontaneously PT-broken phase in the non-Hermitian SSH model, we show that the entanglement entropy for the subsystem of length LA scales as SA = (c/3) ln LA + · · · with c = −2. We show the Jordan block form at the exceptional point leads to the ground state identical to the free Dirac theory As yet another example, we study the entanglement spectrum of the non-Hermitian Chern insulators. Our method provides an alternative way to study the entanglement properties in both critical and topological non-Hermitian systems
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