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The nature of the zero-temperature phase diagram of the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice has been debated in the past three decades, which may hold the key to understand high temperature superconductivity.
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1996
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Rajiv R. P. Singh, Zheng Weihong, C. J. Hamer, and J. Oitmaa, “Dimer order with striped correlations in the J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
1999
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Luca Capriotti and Sandro Sorella, “Spontaneous plaquette dimerization in the J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2000
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Luca Capriotti, Federico Becca, Alberto Parola, and Sandro Sorella, “Resonating valence bond wave functions for strongly frustrated spin systems,” Phys. Rev. Lett. 87
2001
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R. Coldea, S. M. Hayden, G. Aeppli, T. G. Perring, C. D. Frost, T. E. Mason, S.-W. Cheong, and Z. Fisk, “Spin waves and electronic interactions in La 2 CuO 4 {{\rm La}}_{2}{{\rm CuO}}_{4} ,” Phys. Rev. Lett. 86
2001
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R. Melzi, S. Aldrovandi, F. Tedoldi, P. Carretta, P. Millet, and F. Mila, “Magnetic and thermodynamic properties of Li 2 VOSiO 4 {{\rm Li}}_{2}{{\rm VOSiO}}_{4} : A two-dimensional s = 1 / 2 s=1/2 frustrated antiferromagnet on a square lattice,” Phys. Rev. B 64
2001
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H. Rosner, R. R. P. Singh, W. H. Zheng, J. Oitmaa, S.-L. Drechsler, and W. E. Pickett, “Realization of a large J 2 {{J}}_{2} quasi-2d spin-half Heisenberg
2002
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Guang-Ming Zhang, Hui Hu, and Lu Yu, “Valence-bond spin-liquid state in two-dimensional frustrated spin- 1 / 2 1/2 Heisenberg
2003
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Ken’ichi Takano, Yoshiya Kito, Yoshiaki Ōno, and Kazuhiro Sano, “Nonlinear σ \sigma model method for the J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2003
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Alessandro Cuccoli, Tommaso Roscilde, Ruggero Vaia, and Paola Verrucchi, “Detection of XY
2003
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F. Verstraete and J. I. Cirac, “Renormalization algorithms for quantum-many body systems in two and higher dimensions,” (2004), arXiv:cond-mat/0407066 [cond-mat.str-el]
2004
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Patrick A. Lee, Naoto Nagaosa, and Xiao-Gang Wen, “Doping a mott insulator: Physics of high-temperature superconductivity,” Rev. Mod. Phys. 78
2006
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J. Sirker, Zheng Weihong, O. P. Sushkov, and J. Oitmaa, “ J 1 − J 2 {J}_{1}\text{$-$}{J}_{2} model: First-order phase transition versus deconfinement of spinons,” Phys. Rev. B 73
2006
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D. Schmalfuß, R. Darradi, J. Richter, J. Schulenburg, and D. Ihle, “Quantum J 1 {J}_{1} - J 2 {J}_{2} antiferromagnet on a stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering,” Phys. Rev. Lett. 97
2006
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Matthieu Mambrini, Andreas Läuchli, Didier Poilblanc, and Frédéric Mila, “Plaquette valence-bond crystal in the frustrated Heisenberg
2006
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F. Verstraete, M. M. Wolf, D. Perez-Garcia, and J. I. Cirac, “Criticality, the area law, and the computational power of projected entangled pair states,” Phys. Rev. Lett. 96
2006
Cited alongside, same era.
Anders W. Sandvik, “Evidence for deconfined quantum criticality in a two-dimensional Heisenberg
2007
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A. W. Sandvik and G. Vidal, “Variational quantum monte carlo simulations with tensor-network states,” Phys. Rev. Lett. 99
Z. Y. Xie, J. Chen, J. F. Yu, X. Kong, B. Normand, and T. Xiang, “Tensor renormalization of quantum many-body systems using projected entangled simplex states,” Phys. Rev. X 4
2014
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S Vasala, M Avdeev, S Danilkin, O Chmaissem, and M Karppinen, “Magnetic structure of Sr 2 CuWO 6 {{\rm Sr}}_{2}{{\rm CuWO}}_{6} ,” Journal of Physics: Condensed Matter 26
2014
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Satoshi Morita, Ryui Kaneko, and Masatoshi Imada, “Quantum spin liquid in spin 1/2 J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2015
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Johannes Richter, Ronald Zinke, and Damian J. J. Farnell, “The spin-1/2 square-lattice J 1 {J}_{1} - J 2 {J}_{2} model: the spin-gap issue,” The European Physical Journal B 88
2015
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Adam Nahum, J. T. Chalker, P. Serna, M. Ortuño, and A. M. Somoza, “Deconfined quantum criticality, scaling violations, and classical loop models,” Phys. Rev. X 5
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2007
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
2008
Cited alongside, same era.
Marcelo Arlego and Wolfram 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.
F. Verstraete, V. Murg, and J.I. Cirac, “Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems,” Advances in Physics 57
2008
Cited alongside, same era.
Norbert Schuch, Michael M. Wolf, Frank Verstraete, and J. Ignacio Cirac, “Simulation of quantum many-body systems with strings of operators and monte carlo tensor contractions,” Phys. Rev. Lett. 100
2008
Cited alongside, same era.
Anders W. Sandvik, “Scale-renormalized matrix-product states for correlated quantum systems,” Phys. Rev. Lett. 101
2008
Cited alongside, same era.
H. C. Jiang, Z. Y. Weng, and T. Xiang, “Accurate determination of tensor network state of quantum lattice models in two dimensions,” Phys. Rev. Lett. 101
2008
Cited alongside, same era.
L. Isaev, G. Ortiz, and J. Dukelsky, “Hierarchical mean-field approach to the J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2009
Cited alongside, same era.
2015
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Ribhu K. Kaul, “Spin nematics, valence-bond solids, and spin liquids in SO ( n ) \mathrm{SO}(n) quantum spin models on the triangular lattice,” Phys. Rev. Lett. 115
2015
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Ho N. Phien, Johann A. Bengua, Hoang D. Tuan, Philippe Corboz, and Román Orús, “Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing,” Phy. Rev. B 92
2015
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Ling Wang, Zheng-Cheng Gu, Frank Verstraete, and Xiao-Gang Wen, “Tensor-product state approach to spin- 1 2 \frac{1}{2} square J 1 {J}_{1} - J 2 {J}_{2} antiferromagnetic Heisenberg
2016
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Hui Shao, Wenan Guo, and Anders W. Sandvik, “Quantum criticality with two length scales,” Science 352
2016
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P. Babkevich, Vamshi M. Katukuri, B. Fåk, S. Rols, T. Fennell, D. Pajić, H. Tanaka, T. Pardini, R. R. P. Singh, A. Mitrushchenkov, O. V. Yazyev, and H. M. Rønnow, “Magnetic excitations and electronic interactions in Sr 2 CuTeO 6 {{\rm Sr}}_{2}{{\rm CuTeO}}_{6} : A spin- 1 / 2 1/2 square lattice Heisenberg
2016
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Tomoyuki Koga, Nobuyuki Kurita, Maxim Avdeev, Sergey Danilkin, Taku J. Sato, and Hidekazu Tanaka, “Magnetic structure of the s = 1 2 s=\frac{1}{2} quasi-two-dimensional square-lattice Heisenberg
2016
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H. C. Walker, O. Mustonen, S. Vasala, D. J. Voneshen, M. D. Le, D. T. Adroja, and M. Karppinen, “Spin wave excitations in the tetragonal double perovskite Sr 2 CuWO 6 {{\rm Sr}}_{2}{{\rm CuWO}}_{6} ,” Phys. Rev. B 94
2016
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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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Wen-Yuan Liu, Shao-Jun Dong, Yong-Jian Han, Guang-Can Guo, and Lixin He, “Gradient optimization of finite projected entangled pair states,” Phys. Rev. B 95
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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Z. Y. Xie, H. J. Liao, R. Z. Huang, H. D. Xie, J. Chen, Z. Y. Liu, and T. Xiang, “Optimized contraction scheme for tensor-network states,” Phy. Rev. B 96
2017
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Ling Wang and Anders W. Sandvik, “Critical level crossings and gapless spin liquid in the square-lattice spin- 1 / 2 1/2 J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2018
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R. Haghshenas and D. N. Sheng, “ u ( 1 ) u(1) -symmetric infinite projected entangled-pair states study of the spin-1/2 square J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2018
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Wen-Yuan Liu, Shaojun Dong, Chao Wang, Yongjian Han, Hong An, Guang-Can Guo, and Lixin He, “Gapless spin liquid ground state of the spin- 1 2 \frac{1}{2} J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2018
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Philippe Corboz, Piotr Czarnik, Geert Kapteijns, and Luca Tagliacozzo, “Finite correlation length scaling with infinite projected entangled-pair states,” Phys. Rev. X 8
2018
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Michael Rader and Andreas M. Läuchli, “Finite correlation length scaling in lorentz-invariant gapless iPEPS
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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Didier Poilblanc, Matthieu Mambrini, and Sylvain Capponi, “Critical colored-RVB states in the frustrated quantum Heisenberg
2019
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Maissam Barkeshli, Parsa Bonderson, Meng Cheng, and Zhenghan Wang, “Symmetry fractionalization, defects, and gauging of topological phases,” Phys. Rev. B 100
2019
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Hai-Jun Liao, Jin-Guo Liu, Lei Wang, and Tao Xiang, “Differentiable programming tensor networks,” Physical Review X 9
2019
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Francesco Ferrari and Federico Becca, “Gapless spin liquid and valence-bond solid in the J 1 {J}_{1} - J 2 {J}_{2} heisenberg model on the square lattice: Insights from singlet and triplet excitations,” Phys. Rev. B 102
2020
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Anders W. Sandvik and Bowen Zhao, “Consistent scaling exponents at the deconfined quantum-critical point,” Chinese Physics Letters 37
2020
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Bowen Zhao, Jun Takahashi, and Anders W. Sandvik, “Comment on “gapless spin liquid ground state of the spin- 1 / 2 1/2 J 1 {J}_{1} - J 2 {J}_{2} Heisenberg
2020
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Yusuke Nomura and Masatoshi Imada, “Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy,” Phys. Rev. X 11
2021
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Juraj Hasik, Didier Poilblanc, and Federico Becca, “Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks,” SciPost Phys. 10
2021
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