When Can Higher-Form Symmetries Be Made On Site

Area of Science:

• Condensed Matter Physics
• High Energy Physics
• Quantum Field Theory

Background:

• Onsiteability of internal symmetries in lattice models is crucial for understanding their physical realization.
• Standard lore equates onsiteability with anomaly-freedom for 0-form symmetries in (1+1)D.
• This equivalence breaks down for higher-form symmetries, where onsite symmetries can still exhibit anomalies.

Purpose of the Study:

• To clarify the conditions for onsiteability of higher-form symmetries in lattice models.
• To establish an equivalence between onsiteability and the possibility of higher gauging.
• To investigate the implications for realizing higher-form symmetries in (2+1)D and generic dimensions.

Main Methods:

• Analysis of 't Hooft anomalies for finite 1-form symmetries in (2+1)D.
• Derivation of necessary conditions for onsiteability using lattice 't Hooft anomalies.
• Conjecture of a general equivalence between onsiteability and higher gauging on lattices.

Main Results:

• A finite 1-form symmetry in (2+1)D is onsiteable if and only if its 't Hooft anomaly satisfies a specific algebraic condition for 1-gauging.
• Onsiteable 1-form symmetries in (2+1)D can be transformed into transversal Pauli operators using ancillas and circuit conjugation.
• New 'lattice anomalies' are identified that obstruct on-site realization of higher-form symmetries beyond higher gauging in the continuum.

Conclusions:

• Onsiteability of higher-form symmetries is directly linked to the possibility of higher gauging.
• The study provides a rigorous framework for understanding and classifying onsiteable higher-form symmetries.
• The findings have implications for the construction and characterization of lattice models with higher-form symmetries.