A systematic construction of gapped non-liquid states

Abstract

Gapped non-liquid state (also known as fracton state) is a very special gapped quantum state of matter that is characterized by a microscopic cellular structure. Such microscopic cellular structure has a macroscopic effect at arbitrary long distances and cannot be removed by renormalization group flow, which makes gapped non-liquid state beyond the description of topological quantum field theory with a finite number of fields. Using Abelian and non-Abelian topological orders in 2-dimensional (2d) space and the different ways to glue them together via their gapped boundaries, we propose a systematic way to construct 3d gapped states (and in other dimensions). The resulting states are called cellular topological states, which include gapped non-liquid states, as well as gapped liquid states in some special cases. Some new fracton states with fractal excitations are constructed even using 2d ${\mathbb{Z}}_2$ topological order. More general cellular topological states can be constructed by connecting 2d domain walls between different 3d topological orders. The constructed cellular topological states can be viewed as fixed-point states for a reverse renormalization of gapped non-liquid states.

arXiv comment11 pages, 14 figures

References in corpus (67)

• Symmetry protected topological orders and the group cohomology of their symmetry group
• Entanglement renormalization
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Quantum Orders and Symmetric Spin Liquids
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Local unitary transformation, long-range quantum entanglement, wave function renormalization, and topological order
• Classifying quantum phases using Matrix Product States and PEPS
• Local stabilizer codes in three dimensions without string logical operators
• Tensor renormalization group approach to 2D classical lattice models
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Symmetry Fractionalization, Defects, and Gauging of Topological Phases
• Quantum Glassiness
• Models for gapped boundaries and domain walls
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Fracton Phases of Matter
• A classification of symmetry enriched topological phases with exactly solvable models
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Topological boundary conditions in abelian Chern-Simons theory
• Symmetry protected topological phases from decorated domain walls
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• Fermions, strings, and gauge fields in lattice spin models
• Topological phases protected by point group symmetry
• Fermionic SPT phases in higher dimensions and bosonization
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Building crystalline topological phases from lower-dimensional states
• Entanglement renormalization and topological order
• Spin TQFTs and fermionic phases of matter
• Gapped Domain Walls, Gapped Boundaries and Topological Degeneracy
• A theory of 2+1D bosonic topological orders
• Anomalous Symmetry Fractionalization and Surface Topological Order
• Symmetry enriched string-nets: Exactly solvable models for SET phases
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Topological quasiparticles and the holographic bulk-edge relation in 2+1D string-net models
• Exactly Solvable Models for Symmetry-Enriched Topological Phases
• Modular extensions of unitary braided fusion categories and 2+1D topological/SPT orders with symmetries
• The Ground State Structure and Modular Transformations of Fractional Quantum Hall States on a Torus
• A classification of 3+1D bosonic topological orders (I): the case when point-like excitations are all bosons
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Boundary Degeneracy of Topological Order
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Boundary-bulk relation in topological orders
• Cage-Net Fracton Models
• Isotropic Layer Construction and Phase Diagram for Fracton Topological Phases
• Ground State Degeneracy of Topological Phases on Open Surfaces
• Classification of 2+1D topological orders and SPT orders for bosonic and fermionic systems with on-site symmetries
• Renormalization group constructions of topological quantum liquids and beyond
• Emergence of helicity +/- 2 modes (gravitons) from qubit models
• A classification of 3+1D bosonic topological orders (II): the case when some point-like excitations are fermions
• Universal entanglement signatures of foliated fracton phases
• A K matrix Construction of Symmetry Enriched Phases of Matter
• Real-space recipes for general topological crystalline states
• On invariants of Modular categories beyond modular data
• Anisotropic layer construction of anisotropic fracton models
• Topological non-linear $\sigma$-model, higher gauge theory, and a realization of all 3+1D topological orders for boson systems
• Boundary-bulk relation for topological orders as the functor mapping higher categories to their centers
• Symmetry Enriched Phases via Pseudo Anyon Condensation
• Three Dimensional Z2 Topological Phases enriched by Time-Reversal Symmetry
• Boundary Hamiltonian theory for gapped topological orders
• On Enriching the Levin-Wen model with Symmetry
• Gapped domain walls between 2+1D topologically ordered states
• Distinguish modular categories and 2+1D topological orders beyond modular data: Mapping class group of higher genus manifold

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• Long-range entanglement from measuring symmetry-protected topological phases
• Foliated Quantum Field Theory of Fracton Order
• Topological Defect Networks for Fractons of all Types
• Non-Abelian Hybrid Fracton Orders
• Fractonic superfluids. (II). Condensing subdimensional particles
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Type-II fractons from coupled spin chains and layers
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• Optimal Thresholds for Fracton Codes and Random Spin Models with Subsystem Symmetry
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Gapped boundaries and string-like excitations in (3+1)d gauge models of topological phases
• 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
• A degeneracy bound for homogeneous topological order
• Fracton Self-Statistics
• Lattice Clifford fractons and their Chern-Simons-like theory
• Symmetric higher rank topological phases on generic graphs
• Non-Liquid Cellular States
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Fractonic topological phases from coupled wires
• Designer non-Abelian fractons from topological layers
• Fractalizing quantum codes
• Topological defect network representations of fracton stabilizer codes
• Boundary Modes in the Chamon Model
• Hierarchy of Entanglement Renormalization and Long-Range Entangled States
• Foliated order parameter in a fracton phase transition
• Bridging three-dimensional coupled-wire models and cellular topological states: Solvable models for topological and fracton orders
• Weak symmetry breaking and topological order in a 3D compressible quantum liquid
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• Error Resilience of Fracton Codes and Near Saturation of Code-Capacity Threshold in Three Dimensions