Spontaneous breaking of multipole symmetries

Abstract

Multipole symmetries are of interest both as a window on fracton physics and as a crucial ingredient in realizing new universality classes for quantum dynamics. Here we address the question of whether and when multipole symmetries can be spontaneously broken, both in thermal equilibrium and at zero temperature. We derive generalized Mermin-Wagner arguments for the total or partial breaking of multipolar symmetry groups and generalized Imry-Ma arguments for the robustness of such multipolar symmetry breaking to disorder. We present both general results and explicit examples. Our results should be directly applicable to quantum dynamics with multipolar symmetries and also provide a useful stepping stone to understanding the robustness of fracton phases to thermal fluctuations, quantum fluctuations, and disorder.

arXiv comment9 pages. v2: extended the analysis and added a coauthor. v3: clarified some arguments

References in corpus (43)

• Generalized Global Symmetries
• Local stabilizer codes in three dimensions without string logical operators
• Fracton Topological Order, Generalized Lattice Gauge Theory and Duality
• Quantum Glassiness
• Fractons
• Localization from Hilbert space shattering: from theory to physical realizations
• Local constraints can globally shatter Hilbert space: a new route to quantum information protection
• Ergodicity-breaking arising from Hilbert space fragmentation in dipole-conserving Hamiltonians
• 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
• Fracton-Elasticity Duality
• Observing non-ergodicity due to kinetic constraints in tilted Fermi-Hubbard chains
• Fracton hydrodynamics
• Hilbert Space Fragmentation and Commutant Algebras
• Exotic Symmetries, Duality, and Fractons in 2+1-Dimensional Quantum Field Theory
• Exotic $U(1)$ Symmetries, Duality, and Fractons in 3+1-Dimensional Quantum Field Theory
• Anomalous Diffusion in Dipole- and Higher-Moment Conserving Systems
• Statistical localization: from strong fragmentation to strong edge modes
• Subdiffusion and heat transport in a tilted 2D Fermi-Hubbard system
• Towards classification of Fracton phases: the multipole algebra
• Field Theories With a Vector Global Symmetry
• Localization in fractonic random circuits
• Kinetically constrained freezing transition in a dipole-conserving system
• Redundancies in Nambu-Goldstone Bosons
• Generalized Elitzur's Theorem and Dimensional Reduction
• Smectic Liquid Crystals in Random Environments
• Anomalous Subdiffusion from Subsystem Symmetries
• Many body localization with long range interactions
• The low-energy limit of some exotic lattice theories and UV/IR mixing
• Multipole conservation laws and subdiffusion in any dimension
• Fractonic Superfluids
• Crystal-to-Fracton Tensor Gauge Theory Dualities
• Symmetry Enriched Fracton Phases from Supersolid Duality
• Fractons from vector gauge theory
• Scalar Field Theories with Polynomial Shift Symmetries
• Fracton phases via exotic higher-form symmetry-breaking
• Hydrodynamics in lattice models with continuous non-Abelian symmetries
• Quantum smectic gauge theory
• Fractonic superfluids. (II). Condensing subdimensional particles
• Multicritical Symmetry Breaking and Naturalness of Slow Nambu-Goldstone Bosons
• Spontaneously Broken Subsystem Symmetries
• Cascading Multicriticality in Nonrelativistic Spontaneous Symmetry Breaking
• Fractonic gauge theory of smectics

Cited by in corpus (15)

• Generalized Symmetries in Condensed Matter
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• The dipolar Bose-Hubbard model
• Fractonic Luttinger Liquids and Supersolids in a Constrained Bose-Hubbard Model
• Goldstone bosons and fluctuating hydrodynamics with dipole and momentum conservation
• Dipole condensates in tilted Bose-Hubbard chains
• Hohenberg-Mermin-Wagner-type theorems and dipole symmetry
• 2+1d Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• Topological fracton quantum phase transitions by tuning exact tensor network states
• A symmetry principle for gauge theories with fractons
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Detecting Subsystem Symmetry Protected Topological Order Through Strange Correlators
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond