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Conjectures on Hidden Onsager Algebra Symmetries in Interacting Quantum Lattice Models

by Yuan Miao

Submission summary

As Contributors: Yuan Miao
Arxiv Link: (pdf)
Date accepted: 2021-09-06
Date submitted: 2021-07-19 10:59
Submitted by: Miao, Yuan
Submitted to: SciPost Physics
Academic field: Physics
  • Mathematical Physics
  • Quantum Algebra
  • Condensed Matter Physics - Theory
Approach: Theoretical


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)

Author comments upon resubmission

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).

Reports on this Submission

Anonymous Report 2 on 2021-7-20 (Invited Report)


I recommend this version for publication in SciPost.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 1 on 2021-7-19 (Invited Report)


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

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

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