Theory of oblique topological insulators

Benjamin, Moy,; Goldman, Hart; Sohal, Ramanjit; Fradkin, Eduardo

doi:10.48550/arxiv.2206.07725

Cited by 1 publication

(2 citation statements)

References 73 publications

(92 reference statements)

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“…It would be interesting to modify the models for emergent Z N pgauge theory and U (1) p-gauge theory so they can have SPT phases protected by their exact emergent higherform symmetries. In fact, the confined phase (the Z (p) N and U (1) (p) symmetric phases) of these gauge theories becomes an SPT upon adding a topological θ term to the Lagrangian [2,42,43]. Therefore, it would be interesting if one could modify the UV theories of the emergent gauge theory models to have the 2π quantized topological term appear in the mid-IR effective Hamiltonian and investigate the resulting emergent SPT order from a Hamiltonian perspective.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

“…Indeed, abelian topological orders reflect discrete 1-form symmetries spontaneously breaking, and photons in a Coulomb phase arise from U (1) 1-form symmetries spontaneously breaking. A higher-form symmetry can also have a 't Hooft anomaly, providing powerful constraints on the IR through generalized Lieb-Schultz-Mattis-Oshikawa-Hastings theorems and introducing higherform symmetry-protected topological phases [13,14,[34][35][36][37][38][39][40][41][42][43].…”

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confidence: 99%

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Exact emergent higher symmetries in bosonic lattice models

Pace¹,

Wen²

2023

Preprint

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While higher-form symmetries are a powerful tool in studying a quantum many-body system, theories with exact higher-form symmetries are rather special and, in a sense, fine-tuned. This raises an interesting question: can the phases of a microscopic (UV) theory without exact higherform symmetries be exactly characterized by emergent higher-form symmetries? Here we argue the answer is yes by constructing effective theories for bosonic lattice Hamiltonian models that only capture the system's dynamics at E < E scale . The emergent symmetries below this energy scale are then identified as the exact symmetries of this effective theory. We find that the emergent higher-form symmetries (excluding 0-form symmetries) are robust against local UV perturbations and become exact symmetries of the effective theory in the thermodynamic limit. This result is true even for more general higher symmetries, such as non-invertible higher symmetries (i.e., algebraic higher symmetries). Therefore, emergent higher symmetries are exact emergent symmetries: they are not UV symmetries but constrain the IR as if they were. We apply this framework to three lattice models (the quantum clock model and emergent ZN and U (1) p-gauge theory) to identify regions of parameter space with energy scales below which higher-form symmetries, and sometimes associated 't Hooft anomalies, emerge. Since phases of matter are defined in the thermodynamic limit, this implies that a UV theory without exact higher symmetries can have phases exactly characterized by emergent higher symmetries. We discuss in detail the physical consequences of this and contrast it to emergent 0-symmetries, which are never exact. This emphasizes the importance of identifying scale hierarchies and emergent higher symmetries when studying quantum many-body systems.

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Section: Conclusion and Discussionmentioning

confidence: 99%