Field Theories for type-II fractons

@article{Fontana2022FieldTF,
  title={Field Theories for type-II fractons},
  author={Weslei B. Fontana and Pedro R S Gomes and Claudio Chamon},
  journal={SciPost Physics},
  year={2022}
}
We derive an effective field theory for a type-II fracton starting from the Haah code on the lattice. The effective topological theory is not given exclusively in terms of an action; it must be supplemented with a condition that selects physical states. Without the constraint, the action only describes a type-I fracton. The constraint emerges from a condition that cube operators multiply to the identity, and it cannot be consistently implemented in the continuum theory at the operator… 
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References

SHOWING 1-10 OF 66 REFERENCES
Fractonic Chern-Simons and BF theories
TLDR
This paper investigates possible effective field theories for 3D fracton order, by presenting a general philosophy whereby topological-like actions for such higher-rank gauge fields can be constructed.
Quantum field theory of X-cube fracton topological order and robust degeneracy from geometry
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…
Exotic ZN symmetries, duality, and fractons in 3+ 1-dimensional quantum field theory
Following our earlier analyses of nonstandard continuum quantum field theories, we study here gapped systems in 3 + 1 dimensions, which exhibit fractonic behavior. In particular, we present three…
Twisted foliated fracton phases
In the study of three-dimensional gapped models, two-dimensional gapped states should be considered as a free resource. This is the basic idea underlying the notion of `foliated fracton order'…
Fracton Models on General Three-Dimensional Manifolds
Fracton models, a collection of exotic gapped lattice Hamiltonians recently discovered in three spatial dimensions, contain some 'topological' features: they support fractional bulk excitations…
A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
We introduce exactly solvable models of interacting (Majorana) fermions in d≥3 spatial dimensions that realize a new kind of fermion topological quantum order, building on a model presented by S.…
Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics.
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…
Towards Classification of Fracton Phases: The Multipole Algebra
We present an effective field theory approach to the Fracton phases. The approach is based the notion of a multipole algebra. It is an extension of space(-time) symmetries of a charge-conserving…
Symmetric fracton matter: Twisted and enriched
Lattice Clifford fractons and their Chern-Simons-like theory
We use Dirac matrix representations of the Clifford algebra to build fracton models on the lattice and their effective Chern-Simons-like theory. As an example, we build lattice fractons in odd D…
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