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.

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

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• Hilbert Space Fragmentation and Commutant Algebras
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• Quantum smectic gauge theory
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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