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We introduce an entanglement branching operator to split a composite entanglement flow in a tensor network which is a promising theoretical tool for many-body systems.
T. Nishino and K. Okunishi, “Corner Transfer Matrix Renormalization Group Method,” Journal of the Physical Society of Japan 65
1996
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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,” Physical Review Letters 96
2006
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M. Levin and C.P. Nave, “Tensor Renormalization Group Approach to Two-Dimensional Classical Lattice Models,” Physical Review Letters 99
2007
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Z.-C. Gu and X.-G. Wen, “Tensor-entanglement-filtering renormalization approach and symmetry-protected topological order,” Physical Review B 80
2009
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G. Evenbly and G. Vidal, “Algorithms for entanglement renormalization,” Physical Review B 79
2009
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N. Schuch, J.I. Cirac, and D. Perez-Garcia, “PEPS as ground states: Degeneracy and topology,” Annals of Physics 325
2010
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G. Evenbly and G. Vidal, “Frustrated Antiferromagnets with Entanglement Renormalization: Ground State of the Spin-1/2 Heisenberg Model on a Kagome Lattice,” Physical Review Letters 104
2010
Cited alongside, same era.
X. Chen, Z.-C. Gu, and X.-G. Wen, “Classification of gapped symmetric phases in one-dimensional spin systems,” Physical Review B 83
2011
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Z.Y. Xie, J. Chen, M.P. Qin, J.W. Zhu, L.P. Yang, and T. Xiang, “Coarse-graining renormalization by higher-order singular value decomposition,” Physical Review B 86
2012
Cited alongside, same era.
K. Harada, “Numerical study of incommensurability of the spiral state on spin-1/2 spatially anisotropic triangular antiferromagnets using entanglement renormalization,” Physical Review B 86
2012
Cited alongside, same era.
P. Corboz and F. Mila, “Crystals of Bound States in the Magnetization Plateaus of the Shastry-Sutherland Model,” Physical Review Letters 112
H. Ueda, K. Okunishi, and T. Nishino, “Doubling of entanglement spectrum in tensor renormalization group,” Physical Review B 89
2014
Later among the works it cites.
S. Yang, Z.-C. Gu, and X.-G. Wen, “Loop Optimization for Tensor Network Renormalization,” Physical Review Letters 118
2017
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G. Evenbly, “Algorithms for tensor network renormalization,” Physical Review B 95
2017
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M Bal, M Mariën, J Haegeman, and F. Verstraete, “Renormalization Group Flows of Hamiltonians Using Tensor Networks,” Physical Review Letters 118
2017
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Markus Hauru, Clement Delcamp, and Sebastian Mizera, “Renormalization of tensor networks using graph-independent local truncations,” Physical Review B 97
2018
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2014
Cited alongside, same era.
P. Corboz, T.M. Rice, and M. Troyer, “Competing States in the t-J Model: Uniform d-Wave State versus Stripe State,” Physical Review Letters 113
2014
Cited alongside, same era.
G. Vidal, “Entanglement Renormalization,” Physical Review Letters 99
Cited in the paper.
G. Vidal, “Classical Simulation of Infinite-Size Quantum Lattice Systems in One Spatial Dimension,” Physical Review Letters 98
Cited in the paper.
G. Evenbly and G. Vidal, “Tensor Network Renormalization,” Physical Review Letters 115
Cited in the paper.
At much far from a critical point, the precision of a new HOTRG algorithm with EB operators seems to be worse than that of the original HOTRG algorithm. At those points, there is not enough entanglement removed by an EB operator. Then, since the optimization problem is not well defined (see the inset in Fig. 11
Cited in the paper.
G. Evenbly and G. Vidal, “Tensor Network Renormalization Yields the Multiscale Entanglement Renormalization Ansatz,” Physical Review Letters 115
Cited in the paper.