Polarization and entanglement spectrum in non-hermitian systems

Abstract

The entanglement spectrum is a useful tool to study topological phases of matter, and contains valuable information about the ground state of the system. Here, we study its properties for free non-Hermitian systems for both point-gapped and line-gapped phases. While the entanglement spectrum only retains part of the topological information in the former case, it is very similar to Hermitian systems in the latter. In particular, it not only mimics the topological edge modes, but also contains all the information about the polarization, even in systems that are not topological. Furthermore, we show that the Wilson loop is equivalent to the many-body polarization and that it reproduces the phase diagram for the system with open boundaries, despite being computed for a periodic system.

13 pages, 8 figures

References in corpus (9)

• Classification of topological insulators and superconductors in three spatial dimensions
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Topological phases in the non-Hermitian Su-Schrieffer-Heeger model
• Periodic Table for Topological Bands with Non-Hermitian Bernard-LeClair Symmetries
• Topological invariance and global Berry phase in non-Hermitian systems
• Defining a bulk-edge correspondence for non-Hermitian Hamiltonians via singular-value decomposition
• Quantum anomaly, non-Hermitian skin effects, and entanglement entropy in open systems
• Flux insertion, entanglement, and quantized responses
• Numerical calculation of the complex berry phase in non-Hermitian systems

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• Topological Transitions with an Imaginary Aubry-Andre-Harper Potential
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Non-Hermitian Haldane-Hubbard model: Effective description of one- and two-body dissipation
• Thermodynamics and entanglement entropy of the non-Hermitian SSH model
• Electric polarization and its quantization in one-dimensional non-Hermitian chains
• Electronic polarization in non-Bloch band theory
• Mixed higher-order topology and nodal and nodeless flat band topological phases in a superconducting multiorbital model
• Mixedness timescale in non-Hermitian quantum systems
• From Hermitian critical to non-Hermitian point-gapped phases
• Unified Bulk-Entanglement Correspondence in Non-Hermitian Systems
• Entanglement scaling behaviors of free fermions on hyperbolic lattices
• Dynamical Geometry of the Haldane Model under a Quantum Quench