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Fusion approach for quantum integrable system associated with the gl(1|1) Lie superalgebra
by Xiaotian Xu, Wuxiao Wen, Tao Yang, Xin Zhang, Junpeng Cao
Submission summary
| Authors (as registered SciPost users): | Xiaotian Xu |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202510_00026v2 (pdf) |
| Date submitted: | Jan. 19, 2026, 7:50 a.m. |
| Submitted by: | Xiaotian Xu |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
In this work we obtain the exact solution of quantum integrable system associated with the Lie superalgebra gl(1|1), both for periodic and for generic open boundary conditions. By means of the fusion technique we derive a closed set of operator identities among the fused transfer matrices. These identities allow us to determine the complete energy spectrum and the corresponding Bethe ansatz equations of the model. Our approach furnishes a systematic framework for studying the spectra of quantum integrable models based on Lie superalgebras, in particular when the $U(1)$ symmetry is broken. The derivation of the Bethe states from the exact spectrum is also addressed.
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
List of changes
General description of changes and amendments
We thank the referees for their constructive feedback. In response to the comment by Referee 1 that “the results of the present approach are still limited to eigenvalues of the transfer matrix”, we have added a new section (Section 4) in the revised manuscript. This section details the construction of the Bethe states for the model with generic open boundary conditions. The corresponding Bethe state in the periodic case is also provided in Eq. (46). Furthermore, to ensure consistency throughout the paper, we have made the necessary revisions in the main text (the highlighted part) and Appendix D.
General description of changes and amendments
We thank the referees for their constructive feedback. In response to the comment by Referee 1 that “the results of the present approach are still limited to eigenvalues of the transfer matrix”, we have added a new section (Section 4) in the revised manuscript. This section details the construction of the Bethe states for the model with generic open boundary conditions. The corresponding Bethe state in the periodic case is also provided in Eq. (46). Furthermore, to ensure consistency throughout the paper, we have made the necessary revisions in the main text (the highlighted part) and Appendix D.
Current status:
Refereeing in preparation