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Non-Unitary Quantum Many-Body Dynamics using the Faber Polynomial Method
by Rafael Diogo Soares, Marco Schirò
Submission summary
| Authors (as registered SciPost users): | Rafael Diogo Soares · Marco Schirò |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/2406.10135v3 (pdf) |
| Date submitted: | 2024-09-13 17:38 |
| Submitted by: | Diogo Soares, Rafael |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approaches: | Theoretical, Computational |
Abstract
Efficient numerical methods are still lacking to probe the unconventional dynamics of quantum many-body systems under non-unitary evolution. In this work, we use Faber polynomials to numerically simulate both the dynamics of non-Hermitian systems and the quantum jumps unravelling of the Lindblad dynamics. We apply the method to the non-interacting and interacting Hatano-Nelson models evolving from two different setups: i) a N\'eel state, and ii) a domain wall. In the first case, we study how interactions preserve the initial magnetic order against the skin effect. In the second example, we present numerical evidence of the existence of an effective hydrodynamic description for the domain-wall melting problem in the non-interacting limit. Additionally, we investigate both the conditional and unconditional dynamics of the quantum jump unravelling in two quantum spin chains, which exhibit either the non-Hermitian or the Liouvillian skin effect. This numerical method inherently generalises the well-established method based on Chebyshev polynomials to accommodate non-Hermitian scenarios.
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
- We have included a comment about hermitization techniques in the introduction and another in Sec. 3.0, where we mention the Kernel Polynomial Method.
- We have added a general comment on the advantages of the method compared to methods that rely on the exponentiation of the Hamiltonian.
- Following Referee 1's comment, we have more clearly emphasized in the text that GHD is used only as a phenomenological description of our results.
- We have named the two models used in Sec. 6 and restructured the discussion and figures to clarify which results refer to each model.
- We have included a comment on the applicability of the method to non-Hermitian Floquet problems in the high-frequency limit, where a time-independent Floquet Hamiltonian can be defined.