Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities

Fazza, Lucca; Sulejmanpašić, Tin

doi:10.48550/arxiv.2211.13047

2022

DOI: 10.48550/arxiv.2211.13047

|View full text |Cite

Preprint

Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities

Lucca Fazza¹,

Tin Sulejmanpašić²

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2023

Publication Types

Select...

Other1

Relationship

Self Cite0

Independent1

Authors

Journals

Cited by 1 publication

(1 citation statement)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…20. One could instead consider a Villain type Hamiltonian model for which these topological defects are observable even in the UV/mid-IR[68][69][70]. Nevertheless, these different UV lattice models should have the same IR effective field theory.…”

mentioning

confidence: 99%

Exact emergent higher symmetries in bosonic lattice models

Pace¹,

Wen²

2023

Preprint

View full text Add to dashboard Cite

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.

show abstract

mentioning

confidence: 99%

Exact emergent higher symmetries in bosonic lattice models

Pace¹,

Wen²

2023

Preprint

View full text Add to dashboard Cite

show abstract

scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.

Contact Info

hi@scite.ai

10624 S. Eastern Ave., Ste. A-614

Henderson, NV 89052, USA

Blog Terms and Conditions API Terms Privacy Policy Contact Cookie Preferences Do Not Sell or Share My Personal Information

Made with 💙 for researchers

Part of the Research Solutions Family.

Lattice Quantum Villain Hamiltonians: Compact scalars, $U(1)$ gauge theories, fracton models and Quantum Ising model dualities

Cited by 1 publication

References 0 publications

Exact emergent higher symmetries in bosonic lattice models

Exact emergent higher symmetries in bosonic lattice models

Contact Info

Product

Resources

About