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Quantum spin liquids can be faithfully represented and efficiently characterized within the framework of Projected Entangled Pair States (PEPS).
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In the supplemental material, we provide several relevant details of this work, including basic knowledge of SU( 3 3 ) group Barut and Raczka 1980 , ED study on various small clusters, DMRG study on finite cylinders, construction of SU( 3 3 ) symmetric PEPS, CTMRG and optimization procedure, additional data for ES, and topological excitation and correlation function of symmetric PEPS. In the end, we also list the nonzero elements of the tensors
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Norbert Schuch, J. Ignacio Cirac, and David Pérez-García, “PEPS as ground states: Degeneracy and topology,” Annals of Physics 325
2010
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2010
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N. Regnault and B. Andrei Bernevig, “Fractional Chern insulator,” Phys. Rev. X , 021014 (2011)
2011
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J. Ignacio Cirac, Didier Poilblanc, Norbert Schuch, and Frank Verstraete, “Entanglement spectrum and boundary theories with projected entangled-pair states,” Physical Review B 83
2011
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B. Bauer, P. Corboz, R. Orús, and M. Troyer, “Implementing global abelian symmetries in projected entangled-pair state algorithms,” Phys. Rev. B 83
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Sukhwinder Singh, Robert N. C. Pfeifer, and Guifre Vidal, “Tensor network states and algorithms in the presence of a global U(1) symmetry,” Phys. Rev. B 83
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Norbert Schuch, Didier Poilblanc, J. Ignacio Cirac, and David Pérez-García, “Resonating valence bond states in the PEPS formalism,” Physical Review B 86
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B. Andrei Bernevig and N. Regnault, “Emergent many-body translational symmetries of Abelian and non-Abelian fractionally filled topological insulators,” Phys. Rev. B 85
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2016
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Didier Poilblanc, Norbert Schuch, and Ian Affleck, “ SU ( 2 ) 1 \mathrm{SU}(2{)}_{1} chiral edge modes of a critical spin liquid,” Phys. Rev. B 93
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Yi Zhou, Kazushi Kanoda, and Tai-Kai Ng, “Quantum spin liquid states,” Rev. Mod. Phys. 89
2017
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H. J. Liao, Z. Y. Xie, J. Chen, Z. Y. Liu, H. D. Xie, R. Z. Huang, B. Normand, and T. Xiang, “Gapless spin-liquid ground state in the s = 1 / 2 s=1/2 kagome antiferromagnet,” Phys. Rev. Lett. 118
2017
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Since our model possesses one SU(3) fermion per unit cell (equivalent to 1/3 filling), a trivial featureless gapped ground-state is impossible according to the Lieb-Schultz-Mattis theorem for SU(N) spin systems and its generalization to two dimensions Lieb et al. 1961 ; Oshikawa 2000 ; Hastings 2005 ; Totsuka 2017 and, hence, a uniform gapped phase has to be topological
2017
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Didier Poilblanc and Matthieu Mambrini, “Quantum critical phase with infinite projected entangled paired states,” Phys. Rev. B 96
2017
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N. Read, “Compactly-supported wannier functions and algebraic k-theory,” Phys. Rev. B 95
2017
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Didier Poilblanc, “Investigation of the chiral antiferromagnetic Heisenberg model using projected entangled pair states,” Phys. Rev. B 96
2017
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Kasper Duivenvoorden, Mohsin Iqbal, Jutho Haegeman, Frank Verstraete, and Norbert Schuch, “Entanglement phases as holographic duals of anyon condensates,” Phys. Rev. B 95
2017
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2017
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Ji-Yao Chen and Didier Poilblanc, “Topological ℤ 2 \mathbb{Z}_{2} resonating-valence-bond spin liquid on the square lattice,” Phys. Rev. B 97
2018
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Ji-Yao Chen, Laurens Vanderstraeten, Sylvain Capponi, and Didier Poilblanc, “Non-abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study,” Phys. Rev. B 98
2018
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Xiao-Yu Dong, Ji-Yao Chen, and Hong-Hao Tu, “Su(3) trimer resonating-valence-bond state on the square lattice,” Phys. Rev. B 98
2018
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M. T. Fishman, L. Vanderstraeten, V. Zauner-Stauber, J. Haegeman, and F. Verstraete, “Faster methods for contracting infinite two-dimensional tensor networks,” Phys. Rev. B 98
2018
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Anna Hackenbroich, Antoine Sterdyniak, and Norbert Schuch, “Interplay of su(2), point group, and translational symmetry for projected entangled pair states: Application to a chiral spin liquid,” Phys. Rev. B 98
2018
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Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, and Naoki Kawashima, “Gapless kitaev spin liquid to classical string gas through tensor networks,” Phys. Rev. Lett. 123
2019
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Ivana Kurečić, Laurens Vanderstraeten, and Norbert Schuch, “Gapped su(3) spin liquid with ℤ 3 \mathbb{Z}_{3} topological order,” Phys. Rev. B 99
2019
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