Emergent fractons and algebraic quantum liquid from plaquette melting transitions

Abstract

Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this work, we study the properties of topological defects in valence plaquette solid (VPS) phases on square and cubic lattices. We show that the defects of the VPS order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints deep in the VPS phase, which has been overlooked previously. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist, can potentially inhibit the condensation of vortices and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by proliferation of spinon dipoles. For example, we argue that a $2d$ VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long range entanglement. Such a bond liquid phase yields a concrete example of the elusive $2d$ Bose metal with symmetry fractionalization. We also study $3d$ valence plaquette and valence cube ordered phase, and demonstrate that the topological defects therein also have fractonic dynamics. Possible nearby phases after melting the valence plaquettes or cubes are also discussed.

References in corpus (76)

• "Deconfined" quantum critical points
• Quantum Error Correction for Quantum Memories
• Quantum criticality beyond the Landau-Ginzburg-Wilson paradigm
• Local stabilizer codes in three dimensions without string logical operators
• Lieb-Schultz-Mattis in Higher Dimensions
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Entanglement entropy of fermions in any dimension and the Widom conjecture
• Fractons
• Violation of the entropic area law for Fermions
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• A New Kind of Topological Quantum Order: A Dimensional Hierarchy of Quasiparticles Built from Stationary Excitations
• Subdimensional Particle Structure of Higher Rank U(1) Spin Liquids
• Deconfined quantum critical points: symmetries and dualities
• Analytic and numerical demonstration of quantum self-correction in the 3D Cubic Code
• Generalized Electromagnetism of Subdimensional Particles: A Spin Liquid Story
• Exotic topological order in fractal spin liquids
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Fracton-Elasticity Duality
• Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression
• Scaling in the Fan of an Unconventional Quantum Critical Point
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Continuous quantum phase transition between an antiferromagnet and a valence-bond-solid in two dimensions; evidence for logarithmic corrections to scaling
• Glassy quantum dynamics in translation invariant fracton models
• Entanglement Entropy and the Fermi Surface
• Ring exchange, the Bose metal, and bosonization in two dimensions
• Fracton Models on General Three-Dimensional Manifolds
• Fracton topological order via coupled layers
• Deconfined Quantum Criticality, Scaling Violations, and Classical Loop Models
• Spinons and triplons in spatially anisotropic frustrated antiferromagnets
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• The phase diagram of the hexagonal lattice quantum dimer model
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Observation of a 4-spin Plaquette Singlet State in the Shastry-Sutherland compound SrCu2(BO3)2
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Emergent Gravity of Fractons: Mach's Principle Revisited
• Chiral Topological Elasticity and Fracton Order
• Quantum Criticality and Deconfinement in Phase Transitions Between Valence Bond Solids
• Localization in fractonic random circuits
• Deconfined quantum criticality and Neel order via dimer disorder
• A lattice model for the SU(N) Neel-VBS quantum phase transition at large N
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Possibility of Deconfined Criticality in SU(N) Heisenberg Models at Small N
• Néel to valence-bond solid transition on the honeycomb lattice: Evidence for deconfined criticality
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Twisted Fracton Models in Three Dimensions
• Cage-Net Fracton Models
• Resonating plaquette phases in large spin cold atom systems
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Deconfined criticality critically defined
• Fractonic line excitations : an inroad from 3d elasticity theory
• Bond algebraic liquid phase in strongly correlated multiflavor cold atom systems
• Plaquette order and deconfined quantum critical point in the spin-1 bilinear-biquadratic Heisenberg model on the honeycomb lattice
• Impurity spin texture at a deconfined quantum critical point
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Symmetry enhanced first-order phase transition in a two-dimensional quantum magnet
• Fracton fusion and statistics
• Symmetry enforced fractonicity and $2d$ quantum crystal melting
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Corrections to scaling in the critical theory of deconfined criticality
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Bose Metals and Insulators on Multi-Leg Ladders with Ring Exchange
• Violation of Entanglement-Area Law in Bosonic Systems with Bose Surfaces: Possible Application to Bose Metals
• Compactifying fracton stabilizer models
• Resonating singlet valence plaquettes
• Study of a hard-core boson model with ring-only interactions
• Impurity spin texture at a Néel-Valence Bond Solid critical point in $d=2$ SU(3) quantum antiferromagnets
• Possible realization of the Exciton Bose Liquid phase in a hard-core boson model with ring-only exchange interactions
• Gauge Structures: From Stabilizer Codes to Continuum Models

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• Holographic View of Mixed-State Symmetry-Protected Topological Phases in Open Quantum Systems
• Non-Fermi liquid induced by Bose metal with protected subsystem symmetries
• Tunable deconfined quantum criticality and interplay of different valence-bond solid phases
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• A Multicritical Point with Infinite Fractal Symmetries
• Fractonic criticality in Rydberg atom arrays
• Spontaneous layering and power-law order in the three-dimensional fully-packed hard-plate lattice gas
• Covariant Fracton Electrodynamics in Six Dimensions
• Subsystem symmetries, critical Bose surface, and immobile excitations in an extended compass model
• Hollow Lattice Tensor Gauge Theories with Bosonic Matter
• Structures of group-15 elemental solids from an effective boundary theory
• Higher-order topological quantum paramagnets