Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry
By Kevin Slagle, Yong Baek Kim. 2017
146 citations recorded by the source corpus.
We propose a quantum field theory description of the X-cube model of fracton topological order. The field theory is not (and cannot be) a topological quantum field theory (TQFT), since unlike the X-cube model, TQFTs are invariant (i.e. symmetric) under continuous spacetime transformations. However, the theory is instead invariant under a certain subgroup of the conformal group. We describe how braiding statistics and ground state degeneracy are reproduced by the field theory, and how the the X-cube Hamiltonian and field theory can be minimally coupled to matter fields. We also show that even on a manifold with trivial topology, spatial curvature can induce a ground state degeneracy that is stable to arbitrary local perturbations! Our formalism may allow for the description of other fracton field theories, where the only necessary input is an equation of motion for a charge density.
Subfields: Atomic and Molecular Physics, and Optics, Condensed Matter Physics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/933dde2e8e9d9e331279cb054ec20c335304f861
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In Atomic and Molecular Physics, and Optics
In Condensed Matter Physics
In Mathematical Physics
Citations in the corpus
- Fracton Models on General Three-Dimensional Manifolds (2017, methodology): “There are hence a large number of “logical operators” that commute with all of the terms in the Hamiltonian and map one ground state to another [14,20].”
- Generalized Symmetries in Condensed Matter (2022, unknown): “Efforts to understand how the rules of ordinary field theory must be relaxed to accommodate such systems and their symmetries have been vigorous (see e.g. (80, 71, 81, 82, 83, 75, 76, 77, 84) and references therein and thereto).”
- Fracton hydrodynamics (2020, background): “[22] Kevin Slagle and Yong Baek Kim, “Quantum field theory of x-cube fracton topological order and robust degeneracy from geometry,” Physical Review B 96, 195139 (2017).”
- Fracton phases of matter (2020, methodology): “(Such a non-Gaussian field theory was also encountered earlier in a field-theoretic treatment of the X-cube model [51].”