Symmetries and anomalies of Kitaev spin-$S$ models: Identifying symmetry-enforced exotic quantum matter

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 $S\in \mathbb{Z}$.

published version

References in corpus (27)

• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Generalized Global Symmetries
• Models and Materials for Generalized Kitaev Magnetism
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Generalized Symmetries in Condensed Matter
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Comments on One-Form Global Symmetries and Their Gauging in 3d and 4d
• Symmetry Protected Topological Phases, Anomalies, and Cobordisms: Beyond Group Cohomology
• Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
• Microscopic mechanism for higher-spin Kitaev model
• Spin-S Kitaev model: Classical Ground States, Order by Disorder and Exact Correlation Functions
• Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
• Anomalies and Symmetry Fractionalization
• Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality
• Pauli topological subsystem codes from Abelian anyon theories
• Generalized Kitaev Models and Slave Genons
• Exact emergent higher-form symmetries in bosonic lattice models
• Unifying Kitaev magnets, kagome dimer models and ruby Rydberg spin liquids
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• ${\mathbb{Z}}_2$ spin liquids in the higher spin-$S$ Kitaev honeycomb model: An exact deconfined ${\mathbb{Z}}_2$ gauge structure in a non-integrable model
• Characterizing Long-Range Entanglement in a Mixed State Through an Emergent Order on the Entangling Surface
• Line Defect Quantum Numbers & Anomalies
• Determining Kitaev interaction in spin-$S$ honeycomb Mott insulators
• Insights into the Anisotropic Spin-$S$ Kitaev Chain
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Phase diagrams of spin-$S$ Kitaev ladders
• Emergent 1-form symmetries

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• Generalizations of Kitaev's honeycomb model from braided fusion categories
• Classical ${\mathbb{Z}}_2$ spin liquid on the generalized four-color Kitaev model
• Exact deconfined gauge structures in the higher-spin Yao-Lee model: a quantum spin-orbital liquid with spin fractionalization and non-Abelian anyons
• Fractionalized Superconductivity Mediated by Majorana Fermions in the Kitaev-Kondo Lattice
• Chiral spin liquid in a generalized Kitaev honeycomb model with ${\mathbb{Z}}_4$ 1-form symmetry
• Even-odd effect in multilayer Kitaev honeycomb magnets