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We study p-string condensation mechanisms for fracton phases from the viewpoint of higher-form symmetry, focusing on the examples of the X-cube model and the rank-two symmetric-tensor U(1) scalar charge theory.
1909
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Cenke Xu, “Gapless bosonic excitation without symmetry breaking: An algebraic spin liquid with soft gravitons,” Phys. Rev. B 74
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2007
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Kevin Slagle, “Foliated quantum field theory of fracton order,” (2020), arXiv:2008.03852 [hep-th]
2008
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Jeongwan Haah, “Local stabilizer codes in three dimensions without string logical operators,” Phys. Rev. A 83
2011
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Sergey Bravyi, Bernhard Leemhuis, and Barbara M. Terhal, “Topological order in an exactly solvable 3d spin model,” Annals of Physics 326
2011
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Xie Chen, Zheng-Xin Liu, and Xiao-Gang Wen, “Two-dimensional symmetry-protected topological orders and their protected gapless edge excitations,” Phys. Rev. B 84
2017
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2018
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Michael Pretko, “The fracton gauge principle,” Phys. Rev. B 98
2018
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Wilbur Shirley, Kevin Slagle, Zhenghan Wang, and Xie Chen, “Fracton models on general three-dimensional manifolds,” Phys. Rev. X 8
2018
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Rahul M. Nandkishore and Michael Hermele, “Fractons,” Annual Review of Condensed Matter Physics 10
2019
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2011
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Zohar Nussinov, Gerardo Ortiz, and Emilio Cobanera, “Effective and exact holographies from symmetries and dualities,” Annals of Physics 327
2012
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Michael Levin and Zheng-Cheng Gu, “Braiding statistics approach to symmetry-protected topological phases,” Phys. Rev. B 86
2012
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Dominic V. Else and Chetan Nayak, “Classifying symmetry-protected topological phases through the anomalous action of the symmetry on the edge,” Phys. Rev. B 90
2014
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Sagar Vijay, Jeongwan Haah, and Liang 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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Davide Gaiotto, Anton Kapustin, Nathan Seiberg, and Brian Willett, “Generalized global symmetries,” Journal of High Energy Physics 2015
2015
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Sagar Vijay, Jeongwan Haah, and Liang Fu, “Fracton topological order, generalized lattice gauge theory, and duality,” Phys. Rev. B 94
2016
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Jeongwan Haah, “Algebraic Methods for Quantum Codes on Lattices,” Revista Colombiana de Matemáticas 50
2016
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Shriya Pai and Michael Hermele, “Fracton fusion and statistics,” Phys. Rev. B 100
2019
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Michael Pretko, Zhengzheng Zhai, and Leo Radzihovsky, “Crystal-to-fracton tensor gauge theory dualities,” Phys. Rev. B 100
2019
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Dominic J. Williamson, Zhen Bi, and Meng Cheng, “Fractonic matter in symmetry-enriched U ( 1 ) {U}(1) gauge theory,” Phys. Rev. B 100
2019
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Zack Weinstein, Gerardo Ortiz, and Zohar Nussinov, “Universality classes of stabilizer code hamiltonians,” Phys. Rev. Lett. 123
2019
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Xiao-Gang Wen, “Emergent anomalous higher symmetries from topological order and from dynamical electromagnetic field in condensed matter systems,” Phys. Rev. B 99
2019
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Michael Pretko, Xie Chen, and Yizhi You, “Fracton phases of matter,” Int. J. Mod. Phys. A 35
2020
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Yizhi You, Trithep Devakul, S. L. Sondhi, and F. J. Burnell, “Fractonic chern-simons and BF theories,” Phys. Rev. Research 2
2020
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Leo Radzihovsky and Michael Hermele, “Fractons from vector gauge theory,” Phys. Rev. Lett. 124
2020
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Vijay B. Shenoy and Roderich Moessner, “ ( k , n ) (k,n) -fractonic maxwell theory,” Phys. Rev. B 101
2020
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Nathan Seiberg, “Field Theories With a Vector Global Symmetry,” SciPost Phys. 8
2020
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Zack Weinstein, Emilio Cobanera, Gerardo Ortiz, and Zohar Nussinov, “Absence of finite temperature phase transitions in the x-cube model and its zp generalization,” Annals of Physics 412
2020
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Lokman Tsui and Xiao-Gang Wen, “Lattice models that realize Z n Z_{n} -1 symmetry-protected topological states for even n n ,” Phys. Rev. B 101
2020
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