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The ground state phase of spin-1/2 $J_1$-$J_2$ antiferromagnetic Heisenberg model on square lattice around the maximally frustrated regime ($J_2\sim 0.5J_1$) has been debated for decades.
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H. J. Schulz and T. A. L. Ziman, Finite-Size Scaling for the Two-Dimensional Frustrated Quantum Heisenberg Antiferromagnet, Europhys. Lett. 18
1992
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T. Einarsson and H. J. Schulz, Direct calculation of the spin stiffness in the J 1 J_{1} - J 2 J_{2} Heisenberg antiferromagnet, Phys. Rev. B 51
1995
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H. J. Schulz, T. A. L. Ziman and D. Poilblanc, Magnetic Order and Disorder in the Frustrated Quantum Heisenberg Antiferromagnet in Two Dimensions, J. Phys. I 6
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L. Capriotti and S. Sorella, Spontaneous Plaquette Dimerization in the J 1 J_{1} - J 2 J_{2} Heisenberg Model, Phys. Rev. Lett. 84
2000
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R. Moessner and S. L. Sondhi, Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model, Phys. Rev. Lett. 86
2001
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2001
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F. Verstraete, and J. I. Cirac, Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions, (2004), eprint arXiv:cond-mat/0407066v1
2004
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2004
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K. S. D. Beach, Master equation approach to computing RVB bond amplitudes, Phys. Rev. B 79
2009
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V. Murg, F. Verstraete and J. I. Cirac, Exploring frustrated spin systems using projected entangled pair states, Phys. Rev. B 79
2009
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J. Richter and J. Schulenburg, The spin-1/2 J 1 J_{1} - J 2 J_{2} Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins, Eur. Phys. J. B 73
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A. W. Sandvik, Continuous Quantum Phase Transition between an Antiferromagnet and a Valence-Bond Solid in Two Dimensions: Evidence for Logarithmic Corrections to Scaling, Phys. Rev. Lett. 104
2010
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B. Pirvu, V. Murg, J. I. Cirac and F. Verstraete, Matrix product operator representations, New J. Phys. 12
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For a review, see P. A. Lee, N. Nagaosa and X. G. Wen, Doping a Mott insulator: Physics of high-temperature superconductivity, Phys. Mod. Phys. 78
2006
Cited alongside, same era.
J. Sirker, Z. Weihong, O. P. Sushkov and J. Oitmaa, J 1 J_{1} - J 2 J_{2} model: First-order phase transition versus deconfinement of spinons, Phys. Rev. B 73
2006
Cited alongside, same era.
M. Mambrini, A. Läuchli, D. Poilblanc and F. Mila, Plaquette valence-bond crystal in the frustrated Heisenberg quantum antiferromagnet on the square lattice, Phys. Rev. B 74
2006
Cited alongside, same era.
A. W. Sandvik, Evidence for Deconfined Quantum Criticality in a Two-Dimensional Heisenberg Model with Four-Spin Interactions, Phys. Rev. Lett. 98
2007
Cited alongside, same era.
M. Levin and C. P. Nave, Phys. Rev. Lett. 99
2007
Cited alongside, same era.
M. Arlego and W. Brenig, Plaquette order in the J 1 J_{1} - J 2 J_{2} - J 3 J_{3} model: Series expansion analysis, Phys. Rev. B 78
2008
Cited alongside, same era.
R. Darradi, O. Derzhko, R. Zinke, J. Schulenburg, S. E. Krüger and J. Richter, Ground state phases of the spin-1/2 J 1 J_{1} - J 2 J_{2} Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment, Phys. Rev. B 78
2008
Cited alongside, same era.
Later among the works it cites.
2011
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2011
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L. Wang, I. Pižorn and F. Verstraete, Monte Carlo simulation with tensor network states, Phys. Rev. B 83
2011
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H.-C. Jiang, H. Yao and L. Balents, Spin Liquid Ground State of the Spin-1/2 Square J 1 J_{1} - J 2 J_{2} Heisenberg Model, Phys. Rev. B 86
2012
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W.-J. Hu, F. Becca, A. Parola, and S. Sorella, Direct evidence for a gapless Z 2 Z_{2} spin liquid by frustrating Néel antiferromagnetism, Phys. Rev. B 88
2013
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L. Wang, D. Poilblanc, Z.-C. Gu, X.-G. Wen and F. Verstraete, Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice, Phys. Rev. Lett. 111
2013
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S.-S. Gong, W. Zhu, D. N. Sheng, O. I. Motrunich and M. P. A. Fisher, Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model, Phys. Rev. Lett. 113
2014
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H. Shao, W. Guo and A. W. Sandvik, Quantum criticality with two length scales, Science 352
2016
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