Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble

Abstract

Entanglement entropy is a powerful tool in characterizing universal features in quantum many-body systems. In quantum chaotic Hermitian systems, typical eigenstates have near maximal entanglement with very small fluctuations. Here, we show that for Hamiltonians displaying non-Hermitian many-body quantum chaos, modeled by the Ginibre ensemble, the entanglement entropy of typical eigenstates is greatly suppressed. The entropy does not grow with the Hilbert space dimension for sufficiently large systems and the fluctuations are of equal order. We derive the novel entanglement spectrum that has infinite support in the complex plane and strong energy dependence. We provide evidence of universality and similar behavior is found in the non-Hermitian Sachdev-Ye-Kitaev (nSYK) model, indicating the general applicability of the Ginibre ensemble to dissipative many-body quantum chaos.

5 pages, 4 figures; v2: universality results added, background on Dyson Brownian Motion and alternative definition of von Neumann entropy added to supplemental material, references added, and other minor revisions to match version published in PRL

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• Statistical mechanics for non-Hermitian quantum systems
• Krylov space approach to Singular Value Decomposition in non-Hermitian systems
• Field theory of non-Hermitian disordered systems
• Quantum entanglement and non-Hermiticity in free-fermion systems
• Probing quantum chaos through singular-value correlations in sparse non-Hermitian SYK model
• Multifractality of many-body non-Hermitian skin effect
• Eigenvector Correlations Across the Localisation Transition in non-Hermitian Power-Law Banded Random Matrices
• Singular Value Decomposition and Its Blind Spot for Quantum Chaos in Non-Hermitian Sachdev-Ye-Kitaev Models
• Non-Abelian entanglement asymmetry in random states
• Complex entanglement entropy for complex conformal field theory
• Three perspectives on entropy dynamics in a non-Hermitian two-state system
• Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
• Short-time behavior of a system ruled by non-Hermitian time-dependent Hamiltonians
• Determining non-Hermitian parent Hamiltonian from a single eigenstate
• Open-system dynamics in local Lindbladians with chaotic spectra
• Non-linear sigma models for non-Hermitian random matrices in symmetry classes AI${}^{†}$ and AII${}^{†}$
• Entanglement production in the Sachdev-Ye-Kitaev Model and its variants
• Asymptotically exact solution of the non-Hermitian disordered interacting Hatano-Nelson chain