Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
arXiv:2504.08557 · doi:10.21468/SciPostPhys.19.4.094
Abstract
Non-Hermitian quantum many-body systems feature steady-state entanglement transitions driven by the competition between unitary dynamics and dissipation. In this work, we reveal the fundamental role of conservation laws in shaping this competition. Focusing on translation-invariant non-interacting fermionic models with U(1) symmetry, we present a theoretical framework to understand the structure of the steady-state of these models and their entanglement content based on two ingredients: the nature of the spectrum of the non-Hermitian Hamiltonian and the constraints imposed on the steady-state single-particle occupation by the conserved quantities. These emerge from an interplay between Hamiltonian symmetries and initial state, due to the non-linearity of measurement back-action. For models with complex energy spectrum, we show that the steady state is obtained by filling single-particle right eigenstates with the largest imaginary part of the eigenvalue. As a result, one can have partially filled or fully filled bands in the steady-state, leading to an entanglement entropy undergoing a filling-driven transition between critical sub volume scaling and area-law, similar to ground-state problems. Conversely, when the spectrum is fully real, we provide evidence that local observables can be captured using a diagonal ensemble, and the entanglement entropy exhibits a volume-law scaling independently on the initial state, akin to unitary dynamics. We illustrate these principles in the Hatano-Nelson model with periodic boundary conditions and the non-Hermitian Su-Schrieffer-Heeger model, uncovering a rich interplay between the single-particle spectrum and conservation laws in determining the steady-state structure and the entanglement transitions. These conclusions are supported by exact analytical calculations and numerical calculations relying on the Faber polynomial method.
41 pages, 15 figures; Resubmission to SciPost, minor changes. Comments are welcome
References in corpus (21)
- Thermalization and its mechanism for generic isolated quantum systems
- Quantum trajectories and open many-body quantum systems
- Entanglement Phase Transition Induced by the Non-Hermitian Skin Effect
- Entanglement and charge-sharpening transitions in U(1) symmetric monitored quantum circuits
- Universal corrections to scaling for block entanglement in spin-1/2 XX chains
- Volume-to-Area Law Entanglement Transition in a non-Hermitian Free Fermionic Chain
- Volume-law to area-law entanglement transition in a non-unitary periodic Gaussian circuit
- Dynamics of entanglement after exceptional quantum quench
- Entanglement Dynamics in Monitored Systems and the Role of Quantum Jumps
- Entanglement Entropy of Non-Hermitian Eigenstates and the Ginibre Ensemble
- Relaxation to a Parity-Time Symmetric Generalized Gibbs Ensemble after a Quantum Quench in a Driven-Dissipative Kitaev Chain
- Entanglement dynamics in the many-body Hatano-Nelson model
- Measurement-induced symmetry restoration and quantum Mpemba effect
- Non-Hermitian Hamiltonians Violate the Eigenstate Thermalization Hypothesis
- Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
- Entanglement Transition due to particle losses in a monitored fermionic chain
- Dynamics and Phases of Nonunitary Floquet Transverse-Field Ising Model
- Dynamics of monitored SSH Model in Krylov Space: From Complexity to Quantum Fisher Information
- Quantum quenches in driven-dissipative quadratic fermionic systems with parity-time symmetry
- Phase transitions in a non-Hermitian Su-Schrieffer-Heeger model via Krylov spread complexity
- Unveiling Eigenstate Thermalization for Non-Hermitian systems