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We formulate and prove the local twist version of the Yamanaka-Oshikawa-Affleck theorem, an extension of the Lieb-Schultz-Mattis theorem, for one-dimensional systems of quantum particles or spins.
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1961
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F.D.M. Haldane, Nonlinear field theory of large-spin Heisenberg antiferromagnets: semiclassically quantized solitons of the one-dimensional easy-axis Néel state
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M. Yamanaka, M. Oshikawa, and I. Affleck, Nonperturbative approach to Luttinger’s theorem in one dimension
1997
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M. Oshikawa, private communication (1997)
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T. Koma, Spectral gaps of quantum Hall systems with interactions
2000
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M. Oshikawa, Commensurability, excitation gap, and topology in quantum many-particle systems on a periodic lattice
2000
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M.B. Hastings, Lieb-Schultz-Mattis in higher dimensions
2004
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H. Tasaki, Low-lying excitations in one-dimensional lattice electron systems
2004
X.-G. Wen, Quantum Field Theory of Many-Body Systems: From the Origin of Sound to an Origin of Light and Electrons
2007
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2013
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K. Nomura, J. Morishige, and T. Isoyama, Extension of the Lieb-Schultz-Mattis theorem
2015
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H. Watanabe, H.C. Po, A. Vishwanath, and M.P. Zaletel, Filling constraints for spin-orbit coupled insulators in symmorphic and nonsymmorphic crystals
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M.B. Hastings, Sufficient conditions for topological order in insulators
2005
Cited alongside, same era.
B. Nachtergaele and R. Sims, A multi-dimensional Lieb-Schultz-Mattis theorem
2007
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Cited in the paper.
2015
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X.-G. Wen, Zoo of quantum-topological phases of matter
2016
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