Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies

Abstract

The study of gapped quantum many-body systems in three spatial dimensions has uncovered the existence of quantum states hosting quasiparticles that are confined, not by energetics but by the structure of local operators, to move along lower dimensional submanifolds. These so-called "fracton" phases are beyond the usual topological quantum field theory description, and thus require new theoretical frameworks to describe them. Here we consider coupling fracton models to topological quantum field theories in (3+1) dimensions by starting with two copies of a known fracton model and gauging the ${\mathbb{Z}}_2$ symmetry that exchanges the two copies. This yields a class of exactly solvable lattice models that we study in detail for the case of the X-cube model and Haah's cubic code. The resulting phases host finite-energy non-Abelian immobile quasiparticles with robust degeneracies that depend on their relative positions. The phases also host non-Abelian string excitations with robust degeneracies that depend on the string geometry. Applying the construction to Haah's cubic code in particular provides an exactly solvable model with finite energy yet immobile non-Abelian quasiparticles that can only be created at the corners of operators with fractal support.

arXiv comment29+9 pages, 28+5 figures

References in corpus (48)

• Fault-tolerant quantum computation by anyons
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Quantum Glassiness
• Fractons
• 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
• 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
• Glassy quantum dynamics in translation invariant fracton models
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Fractal symmetries: Ungauging the cubic code
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Theory of Twist Liquids: Gauging an Anyonic Symmetry
• Emergent Phases of Fractonic Matter
• Fracton topological phases from strongly coupled spin chains
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Fractional excitations in foliated fracton phases
• Commuting Pauli Hamiltonians as maps between free modules
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Twisted Fracton Models in Three Dimensions
• Quantum mechanical and information theoretic view on classical glass transitions
• Cage-Net Fracton Models
• Fractons from Partons
• Symmetric Tensor Gauge Theories on Curved Spaces
• Correlation function diagnostics for type-I fracton phases
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• $U(1)\times U(1)⋊Z_2$ Chern-Simons Theory and Z_4 Parafermion Fractional Quantum Hall States
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Universal entanglement signatures of foliated fracton phases
• Bilayer quantum Hall phase transitions and the orbifold non-Abelian fractional quantum Hall states
• Foliated fracton order in the checkerboard model
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Foliated fracton order in the Majorana checkerboard model
• Majorana Quantum Lego, a Route Towards Fracton Matter
• Phase transitions in Z_N gauge theory and twisted Z_N topological phases
• Topological Order and Memory Time in Marginally Self-Correcting Quantum Memory
• Non-Abelian defects in Fracton phase of matter

Cited by in corpus (45)

• Fracton Phases of Matter
• Long-range entanglement from measuring symmetry-protected topological phases
• Foliated Quantum Field Theory of Fracton Order
• Shortest Route to Non-Abelian Topological Order on a Quantum Processor
• Fractonic Superfluids
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Topological Defect Networks for Fractons of all Types
• Twisted foliated fracton phases
• Fracton fusion and statistics
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Non-Abelian Hybrid Fracton Orders
• Anisotropic layer construction of anisotropic fracton models
• Gauging permutation symmetries as a route to non-Abelian fractons
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Fractonic superfluids. (II). Condensing subdimensional particles
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Subsystem symmetry enriched topological order in three dimensions
• Fracton physics of spatially extended excitations
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Type-II fractons from coupled spin chains and layers
• Higher-Rank Tensor Non-Abelian Field Theory: Higher-Moment or Subdimensional Polynomial Global Symmetry, Algebraic Variety, Noether's Theorem, and Gauging
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Non-invertible symmetry-protected topological order in a group-based cluster state
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Non-Abelian Gauged Fracton Matter Field Theory: New Sigma Models, Superfluids and Vortices
• Fracton Self-Statistics
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Designer non-Abelian fractons from topological layers
• Fractalizing quantum codes
• Topological defect network representations of fracton stabilizer codes
• Fracton-like phases from subsystem symmetries
• Emergent fermionic gauge theory and foliated fracton order in the Chamon model
• No Strings Attached: Boundaries and Defects in the Cubic Code
• Strong Hilbert space fragmentation and fractons from subsystem and higher-form symmetries
• Non-Abelian fracton order from gauging a mixture of subsystem and global symmetries
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Fractonic superfluids. III. Hybridizing higher moments
• Gauging Modulated Symmetries via Multiple Gauge Symmetry Operators and Adaptive Quantum Circuits
• Topological Dipole Insulator
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• ${\mathbb{Z}}_N$ generalizations of three-dimensional stabilizer codes
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Covariant Fracton Electrodynamics in Six Dimensions
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes