Emergent Phases of Fractonic Matter

Abstract

Fractons are emergent particles which are immobile in isolation, but which can move together in dipolar pairs or other small clusters. These exotic excitations naturally occur in certain quantum phases of matter described by tensor gauge theories. Previous research has focused on the properties of small numbers of fractons and their interactions, effectively mapping out the "Standard Model" of fractons. In the present work, however, we consider systems with a finite density of either fractons or their dipolar bound states, with a focus on the $U(1)$ fracton models. We study some of the phases in which emergent fractonic matter can exist, thereby initiating the study of the "condensed matter" of fractons. We begin by considering a system with a finite density of fractons, which we show can exhibit microemulsion physics, in which fractons form small-scale clusters emulsed in a phase dominated by long-range repulsion. We then move on to study systems with a finite density of mobile dipoles, which have phases analogous to many conventional condensed matter phases. We focus on two major examples: Fermi liquids and quantum Hall phases. A finite density of fermionic dipoles will form a Fermi surface and enter a Fermi liquid phase. Interestingly, this dipolar Fermi liquid exhibits a finite-temperature phase transition, corresponding to an unbinding transition of fractons. Finally, we study chiral two-dimensional phases corresponding to dipoles in "quantum Hall" states of their emergent magnetic field. We study numerous aspects of these generalized quantum Hall systems, such as their edge theories and ground state degeneracies.

23 pages, 7 figures; close to published version

References in corpus (15)

• Electric Multipole Moments, Topological Multipole Moment Pumping, and Chiral Hinge States in Crystalline Insulators
• $(d-2)$-dimensional edge states of rotation symmetry protected topological states
• Reflection symmetric second-order topological insulators and superconductors
• Local stabilizer codes in three dimensions without string logical operators
• A classification of symmetry enriched topological phases with exactly solvable models
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Higher-Spin Witten Effect and Two-Dimensional Fracton Phases
• Fracton topological phases from strongly coupled spin chains
• Stability of the U(1) spin liquid with spinon Fermi surface in 2+1 dimensions
• Quantized topological terms in weak-coupling gauge theories with symmetry and their connection to symmetry enriched topological phases
• Correlation function diagnostics for type-I fracton phases
• A simple anisotropic three-dimensional quantum spin liquid with fracton topological order
• Finite-Temperature Screening of U(1) Fractons
• General phase spaces: from discrete variables to rotor and continuum limits
• The Weakly Coupled Pfaffian as a Type I Quantum Hall Liquid

Cited by in corpus (80)

• Fractons
• Fracton Phases of Matter
• Fracton-Elasticity Duality
• Fracton hydrodynamics
• The Fracton Gauge Principle
• Foliated fracton order from gauging subsystem symmetries
• Towards classification of Fracton phases: the multipole algebra
• The Higgs Mechanism in Higher-Rank Symmetric $U(1)$ Gauge Theories
• Fractons, dipole symmetries and curved spacetime
• Fracton topological order from Higgs and partial confinement mechanisms of rank-two gauge theory
• Chiral Topological Elasticity and Fracton Order
• Localization in fractonic random circuits
• Topological Entanglement Entropy of Fracton Stabilizer Codes
• Fractional excitations in foliated fracton phases
• Fractal Symmetric Phases of Matter
• Foliated Field Theory and String-Membrane-Net Condensation Picture of Fracton Order
• Twisted Fracton Models in Three Dimensions
• The dipolar Bose-Hubbard model
• Fractonic Matter in Symmetry-Enriched U(1) Gauge Theory
• Cage-Net Fracton Models
• Many-body localization, symmetry, and topology
• Pinch Point Singularities of Tensor Spin Liquids
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Entanglement Entropy From Tensor Network States for Stabilizer Codes
• Topological Defect Networks for Fractons of all Types
• Symmetric Tensor Gauge Theories on Curved Spaces
• Fractonic line excitations : an inroad from 3d elasticity theory
• Recoverable Information and Emergent Conservation Laws in Fracton Stabilizer Codes
• Fractonic Chern-Simons and BF theories
• Higher order topological superconductors as generators of quantum codes
• Volume-preserving diffeomorphism as nonabelian higher-rank gauge symmetry
• Higher Rank Deconfined Quantum Criticality at the Lifshitz Transition and the Exciton Bose Condensate
• Gauging fractons: immobile non-Abelian quasiparticles, fractals, and position-dependent degeneracies
• Braiding and Gapped Boundaries in Fracton Topological Phases
• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
• Anisotropic layer construction of anisotropic fracton models
• Infinite families of fracton fluids with momentum conservation
• Dipole condensates in tilted Bose-Hubbard chains
• Gauging permutation symmetries as a route to non-Abelian fractons
• On duality between Cosserat elasticity and fractons
• Compactifying fracton stabilizer models
• Fractons from polarons
• Entanglement Spectra of Stabilizer Codes: A Window into Gapped Quantum Phases of Matter
• Majorana Quantum Lego, a Route Towards Fracton Matter
• Effective Fractonic Behavior in a Two-Dimensional Exactly Solvable Spin Liquid
• The theory of symmetric tensor field: from fractons to gravitons and back
• Hilbert space fragmentation produces a "fracton Casimir effect"
• Lieb-Schultz-Mattis type constraints on Fractonic Matter
• Gauging fractons and linearized gravity
• A Chern-Simons theory for dipole symmetry
• Generalized $U(1)$ Gauge Field Theories and Fractal Dynamics
• Fractal Quantum Phase Transitions: Critical Phenomena Beyond Renormalization
• Planar p-String Condensation: Chiral Fracton Phases from Fractional Quantum Hall Layers and Beyond
• Fracton physics of spatially extended excitations. II. Polynomial ground state degeneracy of exactly solvable models
• Fractonic gauge theory of smectics
• Quantized Dislocations
• Realization of fractonic quantum phases in the breathing pyrochlore lattice
• Fractons from frustration in hole-doped antiferromagnets
• Lieb Schultz Mattis-Type Theorems and Other Non-perturbative Results for Strongly Correlated Systems with Conserved Dipole Moments
• Anomalous relaxation and hyperuniform fluctuations in center-of-mass conserving systems with broken time-reversal symmetry
• Bose-Hubbard realization of fracton defects
• Fractons from a liquid of singlet pairs
• Non-Abelian defects in Fracton phase of matter
• Holographic subdiffusion
• Spectroscopic fingerprints of gapless type-II fracton phases
• Classical Non-Relativistic Fractons
• Topological order and Fractons from Gauging Exponential Symmetries
• Filling constraints on translation invariant dipole conserving systems
• Hall-like behaviour of higher rank Chern-Simons theory of fractons
• Covariant Interacting Fractons
• Quasi-topological fractons: a 3D dipolar gauge theory
• Fractonic self-duality and covariant magnetic fractons
• Fractonic Quantum Quench in Dipole-constrained Bosons
• Covariant field theory of 3D massive fractons
• Fractons on the edge
• Topological Dipole Insulator
• Unidirectional subsystem symmetry in a hole-doped honeycomb-lattice Ising magnet
• Topological stabilizer models on continuous variables
• Emergent fracton strings from covariant bi-form gauge field theory
• Matrix product state classification of 1D multipole symmetry protected topological phases