Hohenberg-Mermin-Wagner-type theorems and dipole symmetry

Abstract

We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries. For $d$-dimensional systems at a positive temperature, we show that charge symmetry cannot be spontaneously broken for $d\le 4$, while dipole symmetry cannot be spontaneously broken for $d\le 2$. For $T=0$, we show that charge symmetry cannot be spontaneously broken for $d\le 2$ if the compressibility is finite. We also show that continuum systems with a dipole symmetry have infinite inertial mass density.

Reworked introduction and added references

References in corpus (5)

• Local stabilizer codes in three dimensions without string logical operators
• Global Dipole Symmetry, Compact Lifshitz Theory, Tensor Gauge Theory, and Fractons
• The dipolar Bose-Hubbard model
• Spontaneous breaking of multipole symmetries
• Criterion for stability of Goldstone Modes and Fermi Liquid behavior in a metal with broken symmetry

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• A Chern-Simons theory for dipole symmetry
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• Noncommutative Field Theory of the Tkachenko Mode: Symmetries and Decay Rate
• Multipole groups and fracton phenomena on arbitrary crystalline lattices
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• Spontaneous breaking of U(1) symmetry at zero temperature in one dimension
• Hierarchical Proliferation of Higher-Rank Symmetry Defects in Fractonic Superfluids
• Filling constraints on translation invariant dipole conserving systems
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• Fractonic superfluids. III. Hybridizing higher moments
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• Infinite-component $BF$ field theory: Connection of fracton order, Toeplitz braiding, and non-Hermitian amplification
• Preparing Code States via Seed-Entangler-Enriched Sequential Quantum Circuits: Application to Tetra-Digit Topological Error-Correcting Codes