Emergent fermionic gauge theory and foliated fracton order in the Chamon model

Abstract

The Chamon model is an exactly solvable spin Hamiltonian exhibiting nontrivial fracton order. In this work, we dissect two distinct aspects of the model. First, we show that it exhibits an emergent fractonic gauge theory coupled to a fermionic subsystem symmetry-protected topological state under four stacks of ${\mathbb{Z}}_2$ planar symmetries. Second, we show that the Chamon model hosts 4-foliated fracton order by describing an entanglement renormalization group transformation that exfoliates four separate stacks of 2D toric codes from the bulk system.

arXiv comment18 pages, 9 figures

References in corpus (62)

• Fault-tolerant quantum computation by anyons
• Anyons in an exactly solved model and beyond
• Entanglement renormalization
• Topological orders and Edge excitations in FQH states
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• 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
• Quantum orders in an exact soluble model
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• 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
• Fermions, strings, and gauge fields in lattice spin models
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• 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
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Topological Quantum Glassiness
• 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
• Classification of subsystem symmetry-protected topological phases
• The low-energy limit of some exotic lattice theories and UV/IR mixing
• On the energy landscape of 3D spin Hamiltonians with topological order
• Quantum mechanical and information theoretic view on classical glass transitions
• Twisted Fracton Models in Three Dimensions
• Cage-Net Fracton Models
• Symmetric Fracton Matter: Twisted and Enriched
• Fractons from Partons
• Correlation function diagnostics for type-I fracton phases
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Deciphering the nonlocal entanglement entropy of fracton topological orders
• Bifurcation in entanglement renormalization group flow of a gapped spin model
• Fractonic Chern-Simons and BF theories
• Twisted foliated fracton phases
• Localization from superselection rules in translation invariant systems
• Parallelized quantum error correction with fracton topological codes
• Foliated fracton order in the checkerboard model
• Sorting topological stabilizer models in three dimensions
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Non-Abelian Hybrid Fracton Orders
• 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
• Bifurcating entanglement-renormalization group flows of fracton stabilizer models
• Compactifying fracton stabilizer models
• Foliated fracton order in the Majorana checkerboard model
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Fractonic order in infinite-component Chern-Simons gauge theories
• Absence of Finite Temperature Phase Transitions in the X-Cube Model and its ${\mathbb{Z}}_p$ Generalization
• Topological defect network representations of fracton stabilizer codes
• Non-Abelian defects in Fracton phase of matter
• ${\mathbb{Z}}_3$ Topological Order in Face Centered Cubic Quantum Plaquette Model

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• Foliated-Exotic Duality in Fractonic BF Theories
• Fracton Self-Statistics
• Boundary Modes in the Chamon Model
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Planon-modular fracton orders