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Symmetries and anomalies of Kitaev spinS models: Identifying symmetryenforced exotic quantum matter
by Ruizhi Liu, Ho Tat Lam, Han Ma, Liujun Zou
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Submission summary
Authors (as registered SciPost users):  Ho Tat Lam · Han Ma · Liujun Zou 
Submission information  

Preprint Link:  scipost_202312_00042v2 (pdf) 
Date accepted:  20240319 
Date submitted:  20240310 02:41 
Submitted by:  Zou, Liujun 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

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 $\mathbb{Z}_2$ 1form symmetry, denoted by $\mathbb{Z}_2^{[1]}$. There is also an ordinary 0form $\mathbb{Z}_2^{(x)}\times\mathbb{Z}_2^{(y)}\times\mathbb{Z}_2^T$ 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 anomalyfree, while for $S\in\mathbb{Z}+\frac{1}{2}$ there is an anomaly purely associated with the 1form symmetry, but there is no anomaly purely associated with the ordinary symmetry or mixed anomaly between the 0form and 1form 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 1form 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 symmetryenforced 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 ``symmetryenforced 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 spin1/2 case and section on the evenodd 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 spin1/2 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 evenodd 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)