Field Theories for type-II fractons

  title={Field Theories for type-II fractons},
  author={Weslei B. Fontana and Pedro R S Gomes and Claudio Chamon},
  journal={SciPost Physics},
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… 

Figures from this paper

Entanglement in the quantum Hall fluid of dipoles
We revisit a model for gapped fractonic order in (2+1) dimensions (a symmetric-traceless tensor gauge theory with conservation of dipole and trace-quadrupole moments described in [1]) and compute its
Comments on foliated gauge theories and dualities in 3+1d
We investigate the properties of foliated gauge fields and construct several foliated field theories in 3+1d that describe foliated fracton orders both with and without matter, including the recent
Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
In this work we propose a Z N clock model which is exactly solvable on the lattice. We find exotic properties for the low-energy physics, such as UV/IR mixing and excitations with restricted mobility,
Snowmass White Paper: Effective Field Theories for Condensed Matter Systems
We review recent progress and a number of future directions for applications of effective field theory methods to condensed matter systems broadly defined. Our emphasis is on areas that have allowed
Hidden quasiconservation laws in fracton hydrodynamics.
We show that the simplest universality classes of fracton hydrodynamics in more than one spatial dimension, including isotropic theories of charge and dipole conservation, can exhibit hidden


Fractonic Chern-Simons and BF theories
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
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