Topological defect network representations of fracton stabilizer codes

Abstract

A topological defect network (TDN) is formed by a network of topological defects embedded within a topological quantum field theory (TQFT). TDNs were introduced recently for the purpose of describing fracton topological phases of matter using the framework of defect TQFT. Their effectiveness has been demonstrated through numerous examples, yet a systematic construction was lacking. Here we solve this problem by formulating a method to construct TDNs for a wide range of lattice Hamiltonians. Our method takes a lattice Hamiltonian as input, applies an ungauging procedure, then creates a refined lattice within each unit cell, followed by regauging the system to produce a TDN as output. For topological Calderbank-Shor-Steane (CSS) Pauli stabilizer models, this procedure is guaranteed to produce a phase equivalent TDN. This provides TDN representations of canonical fracton models for which no such construction was previously known, including Haah's cubic code and Yoshida's infinite family of fractal spin liquid models. We demonstrate the applicability of our method beyond CSS stabilizer models by constructing TDNs for non-CSS models including Chamon's model and the semionic X-cube model.

arXiv comment31 pages, 8 figures

References in corpus (57)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Good Quantum Error-Correcting Codes Exist
• Multiple Particle Interference and Quantum Error Correction
• Local stabilizer codes in three dimensions without string logical operators
• Braiding statistics approach to symmetry-protected topological phases
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Models for gapped boundaries and domain walls
• 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
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Exotic topological order in fractal spin liquids
• Fracton-Elasticity Duality
• Topological order in an exactly solvable 3D spin model
• The Quantum Double Model with Boundary: Condensations and Symmetries
• Quantum memories at finite temperature
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Glassy quantum dynamics in translation invariant fracton models
• Subsystem symmetry protected topological order
• 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
• Field Theories With a Vector Global Symmetry
• Topological Quantum Glassiness
• Foliated Quantum Field Theory of Fracton Order
• 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
• Classification of subsystem symmetry-protected topological phases
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• On the energy landscape of 3D spin Hamiltonians with topological order
• Twisted Fracton Models in Three Dimensions
• Cage-Net Fracton Models
• Topological Defect Networks for Fractons of all Types
• An invariant of topologically ordered states under local unitary transformations
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Localization from superselection rules in translation invariant systems
• Parallelized quantum error correction with fracton topological codes
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Sorting topological stabilizer models in three dimensions
• Algebraic Methods for Quantum Codes on Lattices
• Non-Abelian Hybrid Fracton Orders
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• A systematic construction of gapped non-liquid states
• Gauging permutation symmetries as a route to non-Abelian fractons
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Subsystem symmetry enriched topological order in three dimensions
• Classification of translation invariant topological Pauli stabilizer codes for prime dimensional qudits on two-dimensional lattices
• Foliated fracton order in the Majorana checkerboard model
• Type-II fractons from coupled spin chains and layers
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Gapped Boundary Theory of the Twisted Gauge Theory Model of Three-Dimensional Topological Orders
• Lattice quantum codes and exotic topological phases of matter

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