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Symmetries, Conservation Laws and Entanglement in Non-Hermitian Fermionic Lattices
by Rafael Diogo Soares, Youenn Le Gal, Chun Y. Leung, Dganit Meidan, Alessandro Romito, Marco Schirò
Submission summary
| Authors (as registered SciPost users): | Rafael Diogo Soares |
| Submission information | |
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| Preprint Link: | scipost_202508_00023v1 (pdf) |
| Date accepted: | Aug. 20, 2025 |
| Date submitted: | Aug. 8, 2025, 4:25 p.m. |
| Submitted by: | Rafael Diogo Soares |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
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.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
List of changes
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We have improved the Conclusion section by discussing how some of the entanglement features observed in our work may behave under other types of dynamics, namely in monitored systems or within the framework of the Lindblad master equation.
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Following Referee 1's comment, we have revised and clarified our use of the term "amplification."
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We have included a new appendix in which we show how the entanglement entropy scales as a function of the subsystem size for different total system sizes in the volume-law phase, for both class B and class C.
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We have corrected the typos found in various parts of the draft.
-We have corrected Fig.10 and improved its color scheme by using the same color for the same value of the filling. This makes it easier to visualise the comparison of entanglement entropy scaling across the different spectral regimes of the SSH model.
- We have improved the references related to the Hartwig-Fisher conjecture in accordance with Referee 2's comments.
Published as SciPost Phys. 19, 094 (2025)