Generalized Elitzur's Theorem and Dimensional Reduction

Abstract

We extend Elitzur's theorem to systems with symmetries intermediate between global and local. In general, our theorem formalizes the idea of {\it dimensional reduction}. We apply the results of this generalization to many systems that are of current interest. These include liquid crystalline phases of Quantum Hall systems, orbital systems, geometrically frustrated spin lattices, Bose metals, and models of superconducting arrays.

10 pages, 1 figure

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• Strong planar subsystem symmetry-protected topological phases and their dual fracton orders
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• Three-dimensional Abelian and non-Abelian gauge Higgs theories
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• Failure of Gutzwiller-type wave function to capture gauge fluctuations: Case study in the Exciton Bose Liquid context
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• Site occupation constraints in mean-field approaches of quantum spin systems at finite temperature
• Majorana stripe order on the surface of a three-dimensional topological insulator
• Topological mass generation in gapless systems
• BCF anomaly and higher-group structure in the low energy effective theories of mesons
• First-order directional ordering transition in the three-dimensional compass model
• Quantum-classical crossover in the spin-1/2 Heisenberg-Kitaev kagome magnet
• Robust Topological Degeneracy of Classical Theories
• Unstable Nambu-Goldstone modes
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• Ground state properties of the Heisenberg-compass model on the square lattice
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