Topological fracton quantum phase transitions by tuning exact tensor network states

Abstract

Gapped fracton phases of matter generalize the concept of topological order and broaden our fundamental understanding of entanglement in quantum many-body systems. However, their analytical or numerical description beyond exactly solvable models remains a formidable challenge. Here we employ an exact 3D quantum tensor-network approach that allows us to study a ${\mathbb{Z}}_N$ generalization of the prototypical X cube fracton model and its quantum phase transitions between distinct topological states via fully tractable wavefunction deformations. We map the (deformed) quantum states exactly to a combination of a classical lattice gauge theory and a plaquette clock model, and employ numerical techniques to calculate various entanglement order parameters. For the ${\mathbb{Z}}_N$ model we find a family of (weakly) first-order fracton confinement transitions that in the limit of $N\to \infty$ converge to a continuous phase transition beyond the Landau-Ginzburg-Wilson paradigm. We also discover a line of 3D conformal quantum critical points (with critical magnetic flux loop fluctuations) which, in the $N\to \infty$ limit, appears to coexist with a gapless deconfined fracton state.

arXiv comment4 + 12 pages, 4 + 9 figures

References in corpus (77)

• Fault-tolerant quantum computation by anyons
• Non-Abelian Anyons and Topological Quantum Computation
• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• "Deconfined" quantum critical points
• Zoo of quantum-topological phases of matter
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• General Relationship Between the Entanglement Spectrum and the Edge State Spectrum of Topological Quantum States
• Coarse-graining renormalization by higher-order singular value decomposition
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Critical behavior of the three-dimensional XY universality class
• Topological Order and Conformal Quantum Critical Points
• Fracton Phases of Matter
• Entanglement spectrum and boundary theories with projected entangled-pair states
• Exotic topological order in fractal spin liquids
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Differentiable Programming Tensor Networks
• Variational optimization with infinite projected entangled-pair states
• The Fracton Gauge Principle
• Gradient methods for variational optimization of projected entangled-pair states
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Field Theories With a Vector Global Symmetry
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Topological order in PEPS: Transfer operator and boundary Hamiltonians
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Strong-weak coupling self-duality in the two-dimensional quantum phase transition of $p+ip$ superconducting arrays
• From classical to quantum dynamics at Rokhsar-Kivelson points
• Foliated Quantum Field Theory of Fracton Order
• Finite Correlation Length Scaling in Lorentz-Invariant Gapless iPEPS Wave Functions
• String and Membrane condensation on 3D lattices
• Finite correlation length scaling with infinite projected entangled-pair states
• Twisted Fracton Models in Three Dimensions
• Exotic ${\mathbb{Z}}_N$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Fractonic Superfluids
• Quantum critical phase with infinite projected entangled paired states
• Resonating plaquette phases in large spin cold atom systems
• Shadows of Anyons
• Topological Defect Networks for Fractons of all Types
• Correlation function diagnostics for type-I fracton phases
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Ordered phase and scaling in $Z_n$ models and the three-state antiferromagnetic Potts model in three dimensions
• Spontaneous breaking of multipole symmetries
• Geometrical String and Spin Systems
• Residual entropies for three-dimensional frustrated spin systems with tensor networks
• Gapless Coulomb state emerging from a self-dual topological tensor-network state
• Entanglement phases as holographic duals of anyon condensates
• Dimensional reduction in superconducting arrays and frustrated magnets
• Dynamics at and near conformal quantum critical points
• SU$(3{)}_1$ Chiral Spin Liquid on the Square Lattice: a View from Symmetric PEPS
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Plaquette Ising models, degeneracy and scaling
• Fractonic superfluids. (II). Condensing subdimensional particles
• Fracton physics of spatially extended excitations
• Hybrid Fracton Phases: Parent Orders for Liquid and Non-Liquid Quantum Phases
• Quantum robustness of fracton phases
• Non-Standard Finite-Size Scaling at First-Order Phase Transitions
• Entanglement order parameters and critical behavior for topological phase transitions and beyond
• Low temperature expansion of the gonihedric Ising model
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Fractonic order in infinite-component Chern-Simons gauge theories
• Subdimensional criticality: condensation of lineons and planons in the X-cube model
• Tensor network approach to phase transitions of a non-Abelian topological phase
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• On the stability of topological order in tensor network states
• Critical behavior of 3D Z(N) lattice gauge theories at zero temperature
• Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
• Competing topological orders in three dimensions: X-cube versus toric code
• Renormalization group analysis on emergence of higher rank symmetry and higher moment conservation
• Quantum phase transition of fracton topological orders
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids

Cited by in corpus (18)

• Magic in generalized Rokhsar-Kivelson wavefunctions
• Robust teleportation of a surface code and cascade of topological quantum phase transitions
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Gaining insights on anyon condensation and 1-form symmetry breaking across a topological phase transition in a deformed toric code model
• Higher-Order Cellular Automata Generated Symmetry-Protected Topological Phases and Detection Through Multi-Point Strange Correlators
• Exotic Symmetry Breaking Properties of Self-Dual Fracton Spin Models
• Quantum Hydrodynamics of Fractonic Superfluids with Lineon Condensate: from Navier-Stokes-like Equations to Landau-like Criterion
• Generalized toric codes on twisted tori for quantum error correction
• Quantum Phase Transitions between Symmetry-Enriched Fracton Phases
• Neural Quantum State Study of Fracton Models
• String-Membrane-Nets from Higher-Form Gauging: An Alternate Route to $p$-String Condensation
• Fractonic criticality in Rydberg atom arrays
• Fractonic superfluids. III. Hybridizing higher moments
• Finite Correlation Length Scaling of Disorder Parameter at Quantum Criticality
• Bridging Rokhsar-Kivelson Type and Generic Quantum Phase Transitions via Thermofield Double States
• There and Back Again: A Gauging Nexus between Topological and Fracton Phases
• 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