SciPost Submission Page
Bethe-State Counting and Witten Index
by Hongfei Shu, Peng Zhao, Rui-Dong Zhu, Hao Zou
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Hao Zou |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202303_00019v2 (pdf) |
| Date accepted: | 2023-07-20 |
| Date submitted: | 2023-06-19 09:11 |
| Submitted by: | Zou, Hao |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approach: | Theoretical |
Abstract
We count the physical Bethe states of quantum integrable models with twisted boundary conditions using the Witten index of 2d supersymmetric gauge theories. For multi-component models solvable by the nested Bethe ansatz, the result is a novel restricted occupancy problem. For the SU(3) spin chain and the t-J model, we propose formulae for the solution count on singular loci in the space of twist parameters.
List of changes
1. In the abstract: “We count the Bethe states … ” to “We count the physical Bethe states …”
2. At the end of the first paragraph of Introduction: we added a footnote [7]: “Not all the Bethe states correspond to the eigenstates of the Hamiltonian, see, for example, [5, 6]. In this paper, we will only count the physical Bethe states. ”
3. In paragraph starting with “A complementary approach …” in the Introduction: we changed “whether Bethe states can be …” to “whether physical Bethe states can be … ”
4. In the paragraph below Equation (9): we changed “We remark that the Bethe states of …” to “We remark that the eigenstates of … ”
5. In the first paragraph of Section IV: we added a word “physical” in the second sentence.
Published as SciPost Phys. 15, 103 (2023)