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Symmetries and anomalies of Kitaev spin-S models: Identifying symmetry-enforced exotic quantum matter
by Ruizhi Liu, Ho Tat Lam, Han Ma, Liujun Zou
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ho Tat Lam · Han Ma · Liujun Zou |
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| Preprint Link: | scipost_202312_00042v2 (pdf) |
| Date accepted: | 2024-03-19 |
| Date submitted: | 2024-03-10 02:41 |
| Submitted by: | Zou, Liujun |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We analyze the internal symmetries and their anomalies in the Kitaev spin-$S$ models. Importantly, these models have a lattice version of a $\mathbb{Z}_2$ 1-form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0-form $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T$ symmetry, where $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}$ are $\pi$ spin rotations around two orthogonal axes, and $\mathbb{Z}_2^T$ is the time reversal symmetry. The anomalies associated with the full $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T\times\mathbb{Z}_2^{[1]}$ symmetry are classified by $\mathbb{Z}_2^{17}$. We find that for $S\in\mathbb{Z}$ the model is anomaly-free, while for $S\in\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1-form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0-form and 1-form symmetries. The consequences of these symmetries and anomalies apply to not only the Kitaev spin-$S$ models, but also any of their perturbed versions, assuming that the perturbations are local and respect the symmetries. If these local perturbations are weak, generically these consequences still apply even if the perturbations break the 1-form symmetry. A notable consequence is that there should generically be a deconfined fermionic excitation carrying no fractional quantum number under the $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T$ symmetry if $S\in\mathbb{Z}+\frac{1}{2}$, which implies symmetry-enforced exotic quantum matter. We also discuss the consequences for $S\in\mathbb{Z}$.
Author comments upon resubmission
List of changes
We made various changes listed below, most of which are to address the comments and questions of the referees.
1. We have changed the title to add the term ``symmetry-enforced exotic quantum matter" to extend the scope of the paper. This phrase is also added in the abstract, introduction, main text and discussion section of the paper.
2. We have restructured the paper, so that the section about the spin-1/2 case and section on the even-odd effect are now combined into a single section.
3. We have expanded Sec. VI to discuss the consequences of the symmetries and anomalies. In particular, we have enumerated more quantum phases compatible with the anomalies that are not known within the Kitaev spin-1/2 model.
4. We have added a sentence to explain the meaning of ``deconfined fermionic excitations" in the language of topological line defects in quantum field theory.
5. We have added a footnote to further explain the interpolation leading to the even-odd effect.
6. We have added a paragraph to explain that our results rely on the assumption that the energy gap to flip the eigenvalue of the $W_p$ operator is finite. This condition holds generically unless the Hamiltonian is fine tuned, so our results are valid for almost all Hamiltonians with the relevant symmetries and anomalies.
7. We have corrected various typos and added some new references.
Published as SciPost Phys. 16, 100 (2024)