Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory

Abstract

Symmetry topological field theory (SymTFT), or topological holography, posits a correspondence between symmetries in a $d$-dimensional theory and topological order in a $(d+1)$-dimensional theory. In this work, we extend this framework to subsystem symmetries and develop subsystem SymTFT as a systematic tool to characterize and classify subsystem symmetry-protected topological (SSPT) phases. For $(2+1)$D gapped phases, we introduce a 2-foliated $(3+1)$D exotic tensor gauge theory (which is equivalent to 2-foliated $(3+1)$D BF theory via exotic duality) as the subsystem SymTFT and systematically analyze its topological boundary conditions and linearly rigid subsystem symmetries. Taking subsystem symmetry groups $G={\mathbb{Z}}_N$ and $G={\mathbb{Z}}_N\times {\mathbb{Z}}_M$ as examples, we demonstrate how to recover the classification scheme $\mathcal{C}[G]=H^2(G^{\times 2},U(1))/{\left(H^2(G,U(1))\right)}^3$, which was previously derived by examining topological invariant under linear subsystem-symmetric local unitary transformations in the lattice Hamiltonian formalism. To illustrate the correspondence between field-theoretic and lattice descriptions, we further analyze ${\mathbb{Z}}_2\times {\mathbb{Z}}_2$ and ${\mathbb{Z}}_N\times {\mathbb{Z}}_M$ cluster state models as concrete examples.

arXiv commentv1: 59 pages; v2: minor revision made

References in corpus (76)

• Topological insulators and superconductors: ten-fold way and dimensional hierarchy
• Periodic table for topological insulators and superconductors
• Generalized Global Symmetries
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Zoo of quantum-topological phases of matter
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Generalized Symmetries in Condensed Matter
• Detection of Symmetry Protected Topological Phases in 1D
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Boson topological insulators: A window into highly entangled quantum phases
• Orbifold groupoids
• Categorical symmetry and non-invertible anomaly in symmetry-breaking and topological phase transitions
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• The Fracton Gauge Principle
• Reflection positivity and invertible topological phases
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Ring exchange, the Bose metal, and bosonization in two dimensions
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Subsystem symmetry protected topological order
• Exactly Soluble Model of a 3D Symmetry Protected Topological Phase of Bosons with Surface Topological Order
• On the classification of topological orders
• AdS/CFT Correspondence And Topological Field Theory
• Foliated fracton order from gauging subsystem symmetries
• Algebraic higher symmetry and categorical symmetry -- a holographic and entanglement view of symmetry
• Field Theories With a Vector Global Symmetry
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Fractal Symmetric Phases of Matter
• Classification of subsystem symmetry-protected topological phases
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• A hierarchy of topological tensor network states
• Lecture Notes on Generalized Symmetries and Applications
• On the cobordism classification of symmetry protected topological phases
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Non-invertible symmetries and LSM-type constraints on a tensor product Hilbert space
• On lattice models of gapped phases with fusion category symmetries
• Symmetry TFTs for 3d QFTs from M-theory
• Cluster state as a non-invertible symmetry protected topological phase
• Anomaly Inflow for Subsystem Symmetries
• Classification of topological phases with finite internal symmetries in all dimensions
• A mathematical theory of gapless edges of 2d topological orders. Part I
• Fractonic Chern-Simons and BF theories
• Fracton phases via exotic higher-form symmetry-breaking
• Higher Form Symmetries TFT in 6d
• Gapped Phases with Non-Invertible Symmetries: (1+1)d
• Subsystem Non-Invertible Symmetry Operators and Defects
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Jordan-Wigner Dualities for Translation-Invariant Hamiltonians in Any Dimension: Emergent Fermions in Fracton Topological Order
• Topological holography, quantum criticality, and boundary states
• Higher-Form Subsystem Symmetry Breaking: Subdimensional Criticality and Fracton Phase Transitions
• Quantum Phases and Transitions in Spin Chains with Non-Invertible Symmetries
• Kitaev lattice models as a Hopf algebra gauge theory
• FCC, Checkerboards, Fractons, and QFT
• Fermionization of fusion category symmetries in 1+1 dimensions
• The Club Sandwich: Gapless Phases and Phase Transitions with Non-Invertible Symmetries
• Searching for Fracton Orders via Symmetry Defect Condensation
• Gauging modulated symmetries: Kramers-Wannier dualities and non-invertible reflections
• Fermion Condensation and Gapped Domain Walls in Topological Orders
• Interaction Enabled Fractonic Higher-Order Topological Phases
• Gapless edge modes in (4+1)-dimensional topologically massive tensor gauge theory and anomaly inflow for subsystem symmetry
• Boson-fermion duality with subsystem symmetry
• Foliated-Exotic Duality in Fractonic BF Theories
• Lattice T-duality from non-invertible symmetries in quantum spin chains
• Spontaneously broken supersymmetric fracton phases with fermionic subsystem symmetries
• Gapped Phases in (2+1)d with Non-Invertible Symmetries: Part I
• Generalized cluster states from Hopf algebras: non-invertible symmetry and Hopf tensor network representation
• Ribbon operators in the generalized Kitaev quantum double model based on Hopf algebras
• Boundary and domain wall theories of 2d generalized quantum double model
• Classification and construction of interacting fractonic higher-order topological phases
• On weak Hopf symmetry and weak Hopf quantum double model
• Fracton-like phases from subsystem symmetries
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Weak Hopf symmetry and tube algebra of the generalized multifusion string-net model

Cited by in corpus (2)

• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
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