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We introduce two exotic lattice models on a general spatial graph.
1901
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1904
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1905
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W. Shirley, K. Slagle, and X. Chen, Twisted foliated fracton phases
1907
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N. Seiberg, Field Theories With a Vector Global Symmetry
1909
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J.-K. Yuan, S. A. Chen, and P. Ye, Fractonic Superfluids
1911
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J. Haah, Local stabilizer codes in three dimensions without string logical operators
1962
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M. Fiedler, Algebraic connectivity of graphs
1973
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F. Y. Wu, Number of spanning trees on a lattice
1977
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G. ’t Hooft, Naturalness, chiral symmetry, and spontaneous chiral symmetry breaking
1980
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M. Y. Khlopov, Fractionally charged particles and quark confinement
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Alexander, S. and Orbach, R., Density of states on fractals : “ fractons ”
1982
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K. A. Berman, Bicycles and spanning trees
1986
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R. Grone and R. Merris, A bound for the complexity of a simple graph
1988
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N. Alon, The number of spanning trees in regular graphs
1990
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D. Dhar, Self-organized critical state of sandpile automaton models
1990
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D. J. Lorenzini, A finite group attached to the laplacian of a graph
1991
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A. Nilli, On the second eigenvalue of a graph
1991
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D. Dhar, P. Ruelle, S. Sen, and D. N. Verma, Algebraic aspects of abelian sandpile models
1995
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Published for the Conference Board of the mathematical sciences by the American Mathematical Society, 1997
F. Chung, Spectral Graph Theory · 1997
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C. L. Henley, Relaxation time for a dimer covering with height representation
1997
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R. Bacher, P. d. La Harpe, and T. Nagnibeda, The lattice of integral flows and the lattice of integral cuts on a finite graph
1997
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N. L. Biggs, Chip-firing and the critical group of a graph
1999
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M. Pretko, X. Chen, and Y. You, Fracton Phases of Matter
2001
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R. Moessner, S. L. Sondhi, and E. Fradkin, Short-ranged resonating valence bond physics, quantum dimer models, and ising gauge theories
2001
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A. Paramekanti, L. Balents, and M. P. A. Fisher, Ring exchange, the exciton bose liquid, and bosonization in two dimensions
2002
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2003
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2004
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W. Shirley, K. Slagle, Z. Wang, and X. Chen, Fracton Models on General Three-Dimensional Manifolds
2018
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AMS Non-Series Monographs. American Mathematical Society, 2018
S. Corry and D. Perkinson, Divisors and Sandpiles: An Introduction to Chip-firing · 2018
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2018
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2018
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2004
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A. Vishwanath, L. Balents, and T. Senthil, Quantum criticality and deconfinement in phase transitions between valence bond solids
2004
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E. Fradkin, D. A. Huse, R. Moessner, V. Oganesyan, and S. L. Sondhi, Bipartite rokhsar–kivelson points and cantor deconfinement
2004
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E. Ardonne, P. Fendley, and E. Fradkin, Topological order and conformal quantum critical points
2004
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C. Chamon, Quantum glassiness in strongly correlated clean systems: An example of topological overprotection
2005
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P. Ghaemi, A. Vishwanath, and T. Senthil, Finite-temperature properties of quantum lifshitz transitions between valence-bond solid phases: An example of local quantum criticality
2005
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P. Gorantla, H. T. Lam, N. Seiberg, and S.-H. Shao, More Exotic Field Theories in 3+1 Dimensions
2007
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M. Baker and S. Norine, Riemann–roch and abel–jacobi theory on a finite graph
2007
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2018
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R. M. Nandkishore and M. Hermele, Fractons
2019
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A. Gromov, Towards classification of Fracton phases: the multipole algebra
2019
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A. Gromov, Chiral Topological Elasticity and Fracton Order
2019
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K. Slagle, A. Prem, and M. Pretko, Symmetric Tensor Gauge Theories on Curved Spaces
2019
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W. Shirley, K. Slagle, and X. Chen, Fractional excitations in foliated fracton phases
2019
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W. Shirley, K. Slagle, and X. Chen, Foliated fracton order in the checkerboard model
2019
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W. Shirley, K. Slagle, and X. Chen, Foliated fracton order from gauging subsystem symmetries
2019
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2019
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P.-S. Hsin and K. Slagle, Comments on foliated gauge theories and dualities in 3+1d
2021
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2021
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2021
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2021
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K. T. Grosvenor, C. Hoyos, F. Peña Benitez, and P. Surówka, Space-Dependent Symmetries and Fractons
2022
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C. Cordova, T. T. Dumitrescu, K. Intriligator, and S.-H. Shao, Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond · 2022
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T. Brauner, S. A. Hartnoll, P. Kovtun, H. Liu, M. Mezei, A. Nicolis, R. Penco, S.-H. Shao, and D. T. Son, Snowmass White Paper: Effective Field Theories for Condensed Matter Systems · 2022
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A. Jain and K. Jensen, Fractons in curved space
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