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We study the possibility of spontaneous symmetry breaking in systems with both charge and dipole symmetries.
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J. Haah, “Local stabilizer codes in three dimensions without string logical operators,” Phys. Rev. A 83
2011
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H. Watanabe and A. Vishwanath, “Criterion for stability of Goldstone modes and Fermi liquid behavior in a metal with broken symmetry,” Proceedings of the National Academy of Sciences 111
2014
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S. Vijay, J. Haah, and L. Fu, “A new kind of topological quantum order: A dimensional hierarchy of quasiparticles built from stationary excitations,” Phys. Rev. B 92
2015
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M. Pretko, “Subdimensional particle structure of higher rank u ( 1 ) u(1) spin liquids,” Phys. Rev. B 95
2017
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K. Jensen and A. Raz, “Large N {N} fractons,” arXiv:2205.01132
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P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, “Global dipole symmetry, compact Lifshitz theory, tensor gauge theory, and fractons,” Phys. Rev. B 106
2022
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C. Stahl, E. Lake, and R. Nandkishore, “Spontaneous breaking of multipole symmetries,” Phys. Rev. B 105
2022
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