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Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models
by Yuan Miao
Submission summary
| Authors (as registered SciPost users): | Yuan Miao |
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| Preprint Link: | https://arxiv.org/abs/2103.14569v4 (pdf) |
| Date accepted: | Sept. 6, 2021 |
| Date submitted: | July 19, 2021, 10:59 a.m. |
| Submitted by: | Yuan Miao |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
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| Approach: | Theoretical |
Abstract
We conjecture the existence of hidden Onsager algebra symmetries in two interacting quantum integrable lattice models, i.e. spin-1/2 XXZ model and spin-1 Zamolodchikov-Fateev model at arbitrary root of unity values of the anisotropy. The conjectures relate the Onsager generators to the conserved charges obtained from semi-cyclic transfer matrices. The conjectures are motivated by two examples which are spin-1/2 XX model and spin-1 U(1)-invariant clock model. A novel construction of the semi-cyclic transfer matrices of spin-1 Zamolodchikov-Fateev model at arbitrary root of unity value of the anisotropy is carried out via transfer matrix fusion procedure.
Author comments upon resubmission
I am grateful to the Referees for for their valuable comments and suggestions. The list of changes are given below.
List of changes
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I have changed the Eq. (4.12) as suggested by the referee. I added Eq. (4.33) in the new version to stress the conjectural nature of the identifications between the canonical generators and generators $\mathbf{Q}_m^r$. I have performed the numerical check that Eq. (4.29) and (4.30) indeed satisfy the presentation $O^\prime$ using the identification of Eq. (4.31). A reference to Eq. (4.4) has been added in front of Eq. (4.32) (in the previous version Eq. (4.31) ).
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A similar comment about the identification between the canonical generators and generators $\mathbf{Q}_m^r$ in Section 6.2 has been added.
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In Eq. (2.7) and (4.12), I have changed the expressions according to the referee's suggestion. I also added the comment about the representation of the quotient of the Onsager algebra in the transverse field Ising model in the line below Eq. (2.7).
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I have changed the notations on the presentations of the Onsager algebra $O$ and $O^\prime$ according to the referee's suggestion throughout the draft.
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I have changed several typos in the main text and the references, especially the one in Eq. (6.11).
Published as SciPost Phys. 11, 066 (2021)