Emergent Gravity of Fractons: Mach's Principle Revisited

Abstract

Recent work has established the existence of stable quantum phases of matter described by symmetric tensor gauge fields, which naturally couple to particles of restricted mobility, such as fractons. We focus on a minimal toy model of a rank 2 tensor gauge field, consisting of fractons coupled to an emergent graviton (massless spin-2 excitation). We show how to reconcile the immobility of fractons with the expected gravitational behavior of the model. First, we reformulate the fracton phenomenon in terms of an emergent center of mass quantum number, and we show how an effective attraction arises from the principles of locality and conservation of center of mass. This interaction between fractons is always attractive and can be recast in geometric language, with a geodesic-like formulation, thereby satisfying the expected properties of a gravitational force. This force will generically be short-ranged, but we discuss how the power-law behavior of Newtonian gravity can arise under certain conditions. We then show that, while an isolated fracton is immobile, fractons are endowed with finite inertia by the presence of a large-scale distribution of other fractons, in a concrete manifestation of Mach's principle. Our formalism provides suggestive hints that matter plays a fundamental role, not only in perturbing, but in creating the background space in which it propagates.

12+4 pages

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Cited by in corpus (103)

• Fractons
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• Fracton-Elasticity Duality
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• The Fracton Gauge Principle
• Quantum Field Theory of X-Cube Fracton Topological Order and Robust Degeneracy from Geometry
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• Fractons, dipole symmetries and curved spacetime
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Localization in fractonic random circuits
• Fracton Topological Order from Nearest-Neighbor Two-Spin Interactions and Dualities
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Emergent Phases of Fractonic Matter
• Dynamical scar states in driven fracton systems
• Foliated Quantum Field Theory of Fracton Order
• Fractional excitations in foliated fracton phases
• Fractal Symmetric Phases of Matter
• X-Cube Fracton Model on Generic Lattices: Phases and Geometric Order
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Pinch Point Singularities of Tensor Spin Liquids
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Symmetric Tensor Gauge Theories on Curved Spaces
• Correlation function diagnostics for type-I fracton phases
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Fractonic line excitations : an inroad from 3d elasticity theory
• Bulk Entanglement Gravity without a Boundary: Towards Finding Einstein's Equation in Hilbert Space
• Twisted foliated fracton phases
• Universal entanglement signatures of foliated fracton phases
• Foliated fracton order in the checkerboard model
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Emergent fractons and algebraic quantum liquid from plaquette melting transitions
• Gravity as a gapless phase and biform symmetries
• Spiral spin-liquid on a honeycomb lattice
• Position-Dependent Excitations and UV/IR Mixing in the ${\mathbb{Z}}_N$ Rank-2 Toric Code and its Low-Energy Effective Field Theory
• Gauging permutation symmetries as a route to non-Abelian fractons
• Fracton hydrodynamics without time-reversal symmetry
• Finite-Temperature Screening of U(1) Fractons
• Compactifying fracton stabilizer models
• $(k,n)$-fractonic Maxwell theory
• Fractons from polarons
• Generalized Symmetries of the Graviton
• Quantum robustness of fracton phases
• Maxwell theory of fractons
• Foliated BF theories and Multipole symmetries
• Hyperbolic Fracton Model, Subsystem Symmetry, and Holography II: The Dual Eight-Vertex Model
• Hilbert space fragmentation produces a "fracton Casimir effect"
• The theory of symmetric tensor field: from fractons to gravitons and back
• Gauging fractons and linearized gravity
• Fractons and exotic symmetries from branes
• Foliated-Exotic Duality in Fractonic BF Theories
• Covariant fracton gauge theory with boundary
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Fracton magnetohydrodynamics
• Deconfinement Dynamics of Fractons in Tilted Bose-Hubbard Chains
• Lattice Clifford fractons and their Chern-Simons-like theory
• Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon
• Fracton gravity from spacetime dipole symmetry
• Fractons, non-Riemannian Geometry, and Double Field Theory
• Fractons from frustration in hole-doped antiferromagnets
• Note on Generalized Symmetries, Gapless Excitations, Generalized Symmetry Protected Topological states, and Anomaly
• Geodesic string condensation from symmetric tensor gauge theory: a unifying framework of holographic toy models
• Entanglement wedge reconstruction and correlation measures in mixed states: modular flows versus quantum recovery channels
• Topological Dipole Conserving Insulators and Multipolar Responses
• Scalar, fermionic and supersymmetric field theories with subsystem symmetries in d+1 dimensions
• Quantum phase transition of fracton topological orders
• Fractalizing quantum codes
• Fractons from a liquid of singlet pairs
• Classical Non-Relativistic Fractons
• Electric Circuit Realizations of Fracton Physics
• Holographic subdiffusion
• Fracton-like phases from subsystem symmetries
• Dynamical Spectral Response of Fractonic Quantum Matter
• Asymptotic symmetries and soft charges of fractons
• Gravitational wave analogues in spin nematics and cold atoms
• Covariant Interacting Fractons
• Line-Graph Approach to Spiral Spin Liquids
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Dynamical Signatures of Rank-2 $U(1)$ Spin Liquids
• On quantum melting of superfluid vortex crystals: from Lifshitz scalar to dual gravity
• Quasi-topological fractons: a 3D dipolar gauge theory
• Foliated order parameter in a fracton phase transition
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Fractonic self-duality and covariant magnetic fractons
• Human-machine collaboration: ordering mechanism of rank-2 spin liquid on breathing pyrochlore lattice
• Corner Modes and Ground-State Degeneracy in Models with Gauge-Like Subsystem Symmetries
• Classical Fractons: Local chaos, global broken ergodicity and an arrow of time
• Fracton and Non-Lorentzian Particle Duality: Gauge Field Couplings and Geometric Implications
• Strings as Hyper-Fractons
• Exploration of The Duality Between Generalized Geometry and Extraordinary Magnetoresistance
• Electric-Magnetic Duality for Symmetric Tensor Gauge Theories and Immobile $p$-branes
• Covariant field theory of 3D massive fractons
• Shift symmetries and duality web in gauge theories
• Global shift symmetry on an ADM hypersurface: Toward emergent gravity
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet
• Emergent fracton strings from covariant bi-form gauge field theory
• Continuum Fractons: Quantization and the Few Body Problem