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The Lieb-Schultz-Mattis (LSM) theorem states that a spin system with translation and spin rotation symmetry and half-integer spin per unit cell does not admit a gapped symmetric ground state lacking fractionalized excitations.
1901
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1907
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Elliott Lieb, Theodore Schultz, and Daniel Mattis, “Two soluble models of an antiferromagnetic chain,” Ann. Phys. 16
1961
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B. Eckmann and P. J. Hilton, “Group-like structures in general categories I multiplications and comultiplications,” Math. Ann. 145
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Kenneth S. Brown, Cohomology of groups (Springer, New York, 1982)
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F.D.M. Haldane, “Continuum dynamics of the 1-D Heisenberg antiferromagnet: Identification with the O(3) nonlinear sigma model,” Phys. Lett. A 93
1983
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Ian Affleck and Elliott H. Lieb, “A proof of part of Haldane’s conjecture on spin chains,” Lett. Math. Phys. 12
1986
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Ian Affleck, Tom Kennedy, Elliott H. Lieb, and Hal Tasaki, “Valence bond ground states in isotropic quantum antiferromagnets,” Commun. Math. Phys. 115
1988
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Wieb Bosma, John Cannon, and Catherine Playoust, “The Magma algebra system I: The user language,” Journal of Symbolic Computation 24
1997
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N. Read and Dmitry Green, “Paired states of fermions in two dimensions with breaking of parity and time-reversal symmetries and the fractional quantum Hall effect,” Phys. Rev. B 61
2000
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A Yu Kitaev, “Unpaired Majorana fermions in quantum wires,” Phys. Usp. 44
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Allen Hatcher, Algebraic topology (Cambridge University Press, Cambridge, 2001)
2001
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M. B. Hastings, “Lieb-Schultz-Mattis in higher dimensions,” Phys. Rev. B 69
2004
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Graham Ellis, “Computing group resolutions,” J. Symbolic Comput. 38
2004
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Alexei Kitaev, “Anyons in an exactly solved model and beyond,” Ann. Phys. 321
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Alexei Kitaev, (2015), Institute for Pure Applied Mathematics, UCLA. http://www.ipam.ucla.edu/abstract/?tid=12389&pcode=STQ2015
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Ryan Thorngren, Combinatorial Topology and Applications to Quantum Field Theory , Ph.D. thesis, UC Berkeley (2018)
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