# Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models

### Submission summary

 As Contributors: Yuan Miao Arxiv Link: https://arxiv.org/abs/2103.14569v4 (pdf) Date accepted: 2021-09-06 Date submitted: 2021-07-19 10:59 Submitted by: Miao, Yuan Submitted to: SciPost Physics Academic field: Physics Specialties: Mathematical Physics Quantum Algebra Condensed Matter Physics - Theory 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.

Published as SciPost Phys. 11, 066 (2021)

Dear referees and editor,

I am grateful to the Referees for for their valuable comments and suggestions. The list of changes are given below.

### List of changes

1. 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) ).

2. A similar comment about the identification between the canonical generators and generators $\mathbf{Q}_m^r$ in Section 6.2 has been added.

3. 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).

4. 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.

5. I have changed several typos in the main text and the references, especially the one in Eq. (6.11).

### Submission & Refereeing History

Resubmission 2103.14569v4 on 19 July 2021
Resubmission 2103.14569v3 on 29 June 2021
Submission 2103.14569v2 on 21 April 2021

## Reports on this Submission

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I recommend this version for publication in SciPost.

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### Report

The author has corrected all points rised in the previous report. I do recommend this new revised version for publication.

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• significance: -
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• clarity: -
• formatting: -
• grammar: -