Field Theories for type-II fractons

Abstract

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 level, but only in a weaker form, in terms of matrix elements of physical states. Informed by these studies and starting from the opposite end, i.e., the continuum, we discuss a Chern-Simons-like theory that does not need a constraint or projector, and yet has no mobile excitations. Whether this continuum theory admits a lattice counterpart remains unanswered.

arXiv comment29 pages, 3 figures

References in corpus (36)

• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Exotic topological order in fractal spin liquids
• Topological order in an exactly solvable 3D spin model
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Glassy quantum dynamics in translation invariant fracton models
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fracton Models on General Three-Dimensional Manifolds
• Towards classification of Fracton phases: the multipole algebra
• Field Theories With a Vector Global Symmetry
• Topological Quantum Glassiness
• Gapless Bosonic Excitation without symmetry breaking: Novel Algebraic Spin liquid with soft Gravitons
• Quantum mechanical and information theoretic view on classical glass transitions
• Emergent Gravity at a Lifshitz Point from a Bose Liquid on the Lattice
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Symmetric Fracton Matter: Twisted and Enriched
• Stable Gapless Bose Liquid Phases without any Symmetry
• Emergence of helicity +/- 2 modes (gravitons) from qubit models
• Fractonic Chern-Simons and BF theories
• Universal entanglement signatures of foliated fracton phases
• Twisted foliated fracton phases
• Anisotropic layer construction of anisotropic fracton models
• A lattice bosonic model as a quantum theory of gravity
• $(k,n)$-fractonic Maxwell theory
• Foliated fracton order in the Majorana checkerboard model
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Distilling Fractons from Layered Subsystem-Symmetry Protected Phases
• Lattice Clifford fractons and their Chern-Simons-like theory
• A Duality Between U(1) Haah Code and 3D Smectic A Phase

Cited by in corpus (1)

• Fractionalizing Global Symmetry on Looplike Topological Excitations