Entangelment Entropy on Generalized Brillouin Zone

TL;DR

This paper explores the entanglement properties of a non-Hermitian SSH model using the Generalized Brillouin Zone, revealing how entanglement entropy relates to topological phases, especially near exceptional points and in non-circular GBZs.

Contribution

It introduces a non-Bloch entanglement entropy framework on the GBZ that recovers bulk-boundary correspondence in non-Hermitian systems and analyzes its behavior near exceptional points.

Findings

Non-Bloch entanglement entropy is well-defined on circular GBZs away from EPs.

Each Fermi point contributes 1 to the central charge in the critical region.

At EPs, the central charge becomes negative due to exceptional bound states.

Abstract

We investigate the entanglement properties of non-Hermitian Su-Schrieffer-Heeger (SSH) model from the perspective of the Generalized Brillouin Zone (GBZ). The non-Bloch entanglement entropy is defined on a quasi-reciprocal lattice, obtained by performing an ordinary Fourier transformation on the non-Bloch Hamiltonian. We demonstrate that the broken bulk-boundary correspondence is recovered in terms of the non-Bloch entanglement entropy. When the GBZ is circular, we show that the non-Bloch entanglement entropy is well-defined (real and positive-definite) in large parameter regions, except close to the exceptional points (EPs). In the critical region, we found that each Fermi point contributes precisely 1 to the central charge $c$ of the logarithmic scaling. At the EP, the central charge becomes negative due to the presence of the exceptional bound state. For the case of non-circular GBZ, long-range hopping emerges in the quasi-reciprocal lattice, and the von Neumann entropy on the GBZ is no longer real. However, the non-Bloch edge entanglement entropy remains real, which serves as a reliable topological indicator and respects the bulk-boundary correspondence. We compute the topological phase diagram, and reveal the critical behavior along the exceptional phase boundaries.