Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators

Abstract

In computer and system sciences, higher-order cellular automata (HOCA) are a type of cellular automata that evolve over multiple time steps and generate complex patterns, which have various applications such as secret sharing schemes, data compression, and image encryption. In this paper, we introduce HOCA to quantum many-body physics and construct a series of symmetry-protected topological (SPT) phases of matter, in which symmetries are supported on a great variety of subsystems embbeded in the SPT bulk. We call these phases HOCA-generated SPT (HGSPT) phases. Specifically, we show that HOCA can generate not only well-understood SPTs with symmetries supported on either regular (e.g., line-like subsystems in the 2D cluster model) or fractal subsystems, but also a large class of unexplored SPTs with symmetries supported on more choices of subsystems. One example is \textit{mixed-subsystem SPT} that has either fractal and line-like subsystem symmetries simultaneously or two distinct types of fractal symmetries simultaneously. Another example is \textit{chaotic-subsystem SPT} in which chaotic-looking symmetries are significantly different from and thus cannot reduce to fractal or regular subsystem symmetries. We also introduce a new notation system to characterize HGSPTs. We prove that all possible subsystem symmetries in square lattice can be locally simulated by an HOCA generated symmetry. As the usual two-point strange correlators are trivial in most HGSPTs, we find that the nontrivial SPT orders can be detected by what we call \textit{multi-point strange correlators}. We propose a universal procedure to design the spatial configuration of the multi-point strange correlators for a given HGSPT phase. Specifically, we find deep connections between multi-point strange correlators and the spurious topological entanglement entropy (STEE), both exhibiting long range behavior in SRE states.

Accepted by PRX Quantum

References in corpus (128)

• Quantum Spin Hall Effect in Graphene
• Topological Insulators in Three Dimensions
• Topological entanglement entropy
• Topological invariants of time-reversal-invariant band structures
• Detecting topological order in a ground state wave function
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Topological phases of fermions in one dimension
• Symmetry protection of topological order in one-dimensional quantum spin systems
• Classifying quantum phases using Matrix Product States and PEPS
• Local stabilizer codes in three dimensions without string logical operators
• Braiding statistics approach to symmetry-protected topological phases
• Topological Phases of One-Dimensional Fermions: An Entanglement Point of View
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Physics of three dimensional bosonic topological insulators: Surface Deconfined Criticality and Quantized Magnetoelectric Effect
• Theory and classification of interacting 'integer' topological phases in two dimensions: A Chern-Simons approach
• 2D symmetry protected topological orders and their protected gapless edge excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Fermionic Symmetry Protected Topological Phases and Cobordisms
• Fracton Phases of Matter
• Symmetry-protected topological orders for interacting fermions -- Fermionic topological nonlinear $\sigma$ models and a special group supercohomology theory
• Exotic topological order in fractal spin liquids
• Symmetry protected topological phases from decorated domain walls
• Classifying gauge anomalies through SPT orders and classifying gravitational anomalies through topological orders
• The Fracton Gauge Principle
• Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge
• Subsystem symmetry protected topological order
• Fracton Models on General Three-Dimensional Manifolds
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Fracton topological order via coupled layers
• Field theory representation of gauge-gravity symmetry-protected topological invariants, group cohomology and beyond
• Gauging spatial symmetries and the classification of topological crystalline phases
• Spin TQFTs and fermionic phases of matter
• Towards classification of Fracton phases: the multipole algebra
• Topological phases with generalized global symmetries
• Interaction effect on topological classification of superconductors in two dimensions
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Field Theories With a Vector Global Symmetry
• Fractons, dipole symmetries and curved spacetime
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Identifying phases of quantum many-body systems that are universal for quantum computation
• A new class of $(2+1)$-d topological superconductor with ${\mathbb{Z}}_8$ topological classification
• Braiding Statistics and Link Invariants of Bosonic/Fermionic Topological Quantum Matter in 2+1 and 3+1 dimensions
• Average Symmetry-Protected Topological Phases
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Classification and Description of Bosonic Symmetry Protected Topological Phases with semiclassical Nonlinear Sigma models
• Foliated Quantum Field Theory of Fracton Order
• Wave Function and Strange Correlator of Short Range Entangled states
• Fractal Symmetric Phases of Matter
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Quantum Walks in artificial electric and gravitational Fields
• Towards a complete classification of fermionic symmetry protected topological phases in 3D and a general group supercohomology theory
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fractonic Superfluids
• Topological states on fractal lattices
• Spurious topological entanglement entropy from subsystem symmetries
• Subsystem symmetries, quantum cellular automata, and computational phases of quantum matter
• Resonating plaquette phases in large spin cold atom systems
• Higher-order topological phases on fractal lattices
• Mapping topological to conformal field theories through strange correlators
• Topological Defect Networks for Fractons of all Types
• Correlation function diagnostics for type-I fracton phases
• Universal quantum computation using fractal symmetry-protected cluster phases
• Global anomalies on the surface of fermionic symmetry-protected topological phases in (3+1) dimensions
• Spurious Long-range Entanglement and Replica Correlation Length
• Hall conductivity of Sierpinski carpet
• Quantum Walks as simulators of neutrino oscillations in vacuum and matter
• Anomaly Inflow for Subsystem Symmetries
• Topological Response Theory of Abelian Symmetry-Protected Topological Phases in Two Dimensions
• Symmetry-protected Topological Phases, Generalized Laughlin Argument and Orientifolds
• Fractonic Chern-Simons and BF theories
• Bona fide interaction-driven topological phase transition in correlated SPT states
• Quantum walks and non-Abelian discrete gauge theory
• Universal Features of Higher-Form Symmetries at Phase Transitions
• Constructing symmetric topological phases of bosons in three dimensions via fermionic projective construction and dyon condensation
• Vortex-line condensation in three dimensions: A physical mechanism for bosonic topological insulators
• A critical lattice model for a Haagerup conformal field theory
• Projective construction of two-dimensional symmetry-protected topological phases with U(1), SO(3), or SU(2) symmetries
• Multi-kink topological terms and charge-binding domain-wall condensation induced symmetry-protected topological states: Beyond Chern-Simons/BF theory
• Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
• Boundary conformal field theory and symmetry protected topological phases in $2+1$ dimensions
• Topological Order, Quantum Codes and Quantum Computation on Fractal Geometries
• Tunneling Topological Vacua via Extended Operators: (Spin-)TQFT Spectra and Boundary Deconfinement in Various Dimensions
• Braiding with Borromean Rings in (3+1)-Dimensional Spacetime
• Topological Paramagnetism in Frustrated Spin-One Mott Insulators
• Quantum Entanglement of Non-Hermitian Quasicrystals
• Optical conductivity of a quantum electron gas in a Sierpinski carpet
• Fractonic superfluids. (II). Condensing subdimensional particles
• Composite Particle Theory of Three-dimensional Gapped Fermionic Phases: Fractional Topological Insulators and Charge-Loop Excitation Symmetry
• Generalized Wen-Zee Terms
• Computational universality of symmetry-protected topologically ordered cluster phases on 2D Archimedean lattices
• $U(1)\times U(1)$ Symmetry Protected Topological Order in Gutzwiller Wave Functions
• Fracton physics of spatially extended excitations
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Quantum Monte Carlo study of strange correlator in interacting topological insulators
• Classifying local fractal subsystem symmetry protected topological phases
• Topological Electromagnetic Responses of Bosonic Quantum Hall, Topological Insulator, and Chiral Semi-Metal phases in All Dimensions
• Topological aspects of the critical three-state Potts model
• Detection of symmetry-protected topological order in AKLT states by exact evaluation of the strange correlator
• On the dynamical behaviour of linear higher-order cellular automata and its decidability
• Fractonic order in infinite-component Chern-Simons gauge theories
• Galois conjugated tensor fusion categories and non-unitary CFT
• Strange correlations in spin-1 Heisenberg antiferromagnets
• Entanglement, non-Hermiticity, and duality
• Topological fracton quantum phase transitions by tuning exact tensor network states
• Universal lower bound on topological entanglement entropy
• Detecting subsystem symmetry protected topological order via entanglement entropy
• Topological phase in $1D$ topological Kondo insulator: $Z_2$ topological insulator, Haldane-like phase and Kondo breakdown
• Fermion confinement via Quantum Walks in 2D+1 and 3D+1 spacetime
• Spin quantum Hall effects in a spin-1 topological paramagnet
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Classical XY Model in 1.99 Dimensions
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Toy model of boundary states with spurious topological entanglement entropy
• Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Geometry defects in Bosonic symmetry protected topological phases
• Strange correlators for topological quantum systems from bulk-boundary correspondence
• Beyond the Freshman's Dream: Classical fractal spin liquids from matrix cellular automata in three-dimensional lattice models
• Field theory of symmetry-protected valence bond solid states in (2+1) dimensions
• Fractalizing quantum codes
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• MERA as a holographic strange correlator
• Non-local finite-depth circuits for constructing SPT states and quantum cellular automata

Cited by in corpus (8)

• Generalized toric codes on twisted tori for quantum error correction
• Entanglement Fractalization
• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• Generalized Statistics on Lattices
• Fractonic superfluids. III. Hybridizing higher moments
• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes
• Spurious Strange Correlators in Symmetry-Protected Topological Phases