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Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics

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arxiv 1806.01855 v1 pith:M5DQHYKZ submitted 2018-06-05 cond-mat.str-el hep-thquant-ph

Daniel Bulmash , Maissam Barkeshli This is my paper · ORCID
classification cond-mat.str-elhep-thquant-ph
keywords theoriesfieldgaugegeneralizedchargeclassdynamicseffective
verification ladder T0 review T1 audit T2 compute T3 formal

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abstract

We present a theoretical framework for a class of generalized $U(1)$ gauge effective field theories. These theories are defined by specifying geometric patterns of charge configurations that can be created by local operators, which then lead to a class of generalized Gauss law constraints. The charge and magnetic excitations in these theories have restricted, subdimensional dynamics, providing a generalization of recently studied higher-rank symmetric $U(1)$ gauge theories to the case where arbitrary spatial rotational symmetries are broken. These theories can describe situations where charges exist at the corners of fractal operators, thus providing a continuum effective field theoretic description of Haah's code and Yoshida's Sierpinski prism model. We also present a $3+1$-dimensional $U(1)$ theory that does not have a non-trivial discrete $\mathbb{Z}_p$ counterpart.

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Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Random Local Stabilizer Codes in Three Dimensions without String or Self-Similar Fractal Logical Operators

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  2. Emergent fractons and algebraic quantum liquid from plaquette melting transitions

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    Topological defects of valence plaquette solid order are fractons, so plaquette melting can proceed via dipole condensation and produce a gapless algebraic bond liquid.

  3. Anisotropic layer construction of anisotropic fracton models

    cond-mat.str-el 2019-08 accept novelty 5.0 of 10

    A coupled-layer construction from stacked 2D toric codes produces an exactly solvable anisotropic fracton model with lineon and planon excitations.

  4. On duality between Cosserat elasticity and fractons

    cond-mat.str-el 2019-08 conditional novelty 4.0 of 10

    A 2D Cosserat elastic medium is dual to a coupled tensor and U(1) gauge theory, with the antisymmetric stress becoming a massive mode and defects showing fracton-like mobility restrictions.

  5. Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond

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    This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.

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