TY  - JOUR
PB  - SciPost Foundation
DO  - 10.21468/SciPostPhys.19.4.094
TI  - Symmetries, conservation laws and entanglement in non-Hermitian fermionic lattices
PY  - 2025/10/13
UR  - https://www.scipost.org/SciPostPhys.19.4.094
JF  - SciPost Physics
JA  - SciPost Phys.
VL  - 19
IS  - 4
SP  - 094
A1  - Diogo Soares, Rafael
AU  - Le Gal, Youenn
AU  - Leung, Chun Y.
AU  - Meidan, Dganit
AU  - Romito, Alessandro
AU  - Schirò, Marco
AB  - 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.
ER  -

@Article{10.21468/SciPostPhys.19.4.094,
	title={{Symmetries, conservation laws and entanglement in non-Hermitian fermionic lattices}},
	author={Rafael D. Soares and Youenn Le Gal and Chun Y. Leung and Dganit Meidan and Alessandro Romito and Marco Schirò},
	journal={SciPost Phys.},
	volume={19},
	pages={094},
	year={2025},
	publisher={SciPost},
	doi={10.21468/SciPostPhys.19.4.094},
	url={https://scipost.org/10.21468/SciPostPhys.19.4.094},
}