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We show a way to perform the canonical renormalization group (RG) prescription in tensor space: write down the tensor RG equation, linearize it around a fixed-point tensor, and diagonalize the resulting linearized RG equation to obtain scaling dimensions.
1912
Earlier work this paper cites.
L. P. Kadanoff, Scaling laws for ising models near T c {T}_{c} , Physics Physique Fizika 2
1966
Earlier work this paper cites.
K. G. Wilson and M. E. Fisher, Critical exponents in 3.99 dimensions, Phys. Rev. Lett. 28
1972
Earlier work this paper cites.
T. Niemeijer and J. M. J. van Leeuwen, Wilson theory for spin systems on a triangular lattice, Phys. Rev. Lett. 31
1973
Earlier work this paper cites.
T. L. Bell and K. G. Wilson, Nonlinear renormalization groups, Phys. Rev. B 10
1974
Earlier work this paper cites.
L. P. Kadanoff, Variational principles and approximate renormalization group calculations, Phys. Rev. Lett. 34
1975
Earlier work this paper cites.
A. Migdal, Recursion equations in gauge field theories 1975 sov. phys, JETP 42
1975
Earlier work this paper cites.
L. P. Kadanoff, Notes on migdal’s recursion formulas, Annals of Physics 100
1976
Earlier work this paper cites.
K. G. Wilson, The renormalization group and critical phenomena, Rev. Mod. Phys. 55
1983
Earlier work this paper cites.
J. L. Cardy, Operator content of two-dimensional conformally invariant theories, Nuclear Physics B 270
1986
Earlier work this paper cites.
J. Polchinski, Scale and conformal invariance in quantum field theory, Nuclear Physics B 303
1988
Earlier work this paper cites.
J. Cardy, Scaling and Renormalization in Statistical Physics , Cambridge Lecture Notes in Physics (Cambridge University Press, 1996) pp. 28–60
1996
Earlier work this paper cites.
P. Di Francesco, P. Mathieu, and D. Sénéchal, Minimal models i, in Conformal Field Theory (Springer New York, New York, NY, 1997)
1997
Earlier work this paper cites.
M. Levin and C. P. Nave, Tensor renormalization group approach to two-dimensional classical lattice models, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
M. Levin, Real space renormalization group and the emergence of topological order (2007), talk at the IPAM workshop “Topological Quantum Computing”
2007
Earlier work this paper cites.
M. Kardar, Statistical Physics of Fields (Cambridge University Press, 2007)
2007
Earlier work this paper cites.
G. Vidal, Entanglement renormalization, Phys. Rev. Lett. 99
2007
Earlier work this paper cites.
M. Hinczewski and A. N. Berker, High-precision thermodynamic and critical properties from tensor renormalization-group flows, Phys. Rev. E 77
2008
Cited alongside, same era.
G. Vidal, Class of quantum many-body states that can be efficiently simulated, Phys. Rev. Lett. 101
2008
Cited alongside, same era.
V. Giovannetti, S. Montangero, and R. Fazio, Quantum multiscale entanglement renormalization ansatz channels, Phys. Rev. Lett. 101
2008
Cited alongside, same era.
Z. Y. Xie, H. C. Jiang, Q. N. Chen, Z. Y. Weng, and T. Xiang, Second renormalization of tensor-network states, Phys. Rev. Lett. 103
2009
Cited alongside, same era.
2009
Cited alongside, same era.
Y. Nakayama, Scale invariance vs conformal invariance, Physics Reports 569
2015
Later among the works it cites.
G. Evenbly and G. Vidal, Tensor network renormalization, Phys. Rev. Lett. 115
2015
Later among the works it cites.
G. Evenbly and G. Vidal, Local scale transformations on the lattice with tensor network renormalization, Phys. Rev. Lett. 116
2016
Later among the works it cites.
S. Yang, Z.-C. Gu, and X.-G. Wen, Loop optimization for tensor network renormalization, Phys. Rev. Lett. 118
2017
Later among the works it cites.
G. Evenbly, Algorithms for tensor network renormalization, Phys. Rev. B 95
2017
Later among the works it cites.
M. Bal, M. Mariën, J. Haegeman, and F. Verstraete, Renormalization group flows of hamiltonians using tensor networks, Phys. Rev. Lett. 118
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2009
Cited alongside, same era.
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2009
Cited alongside, same era.
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2009
Cited alongside, same era.
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2009
Cited alongside, same era.
H. H. Zhao, Z. Y. Xie, Q. N. Chen, Z. C. Wei, J. W. Cai, and T. Xiang, Renormalization of tensor-network states, Phys. Rev. B 81
2010
Cited alongside, same era.
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2010
Cited alongside, same era.
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2011
Cited alongside, same era.
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Later among the works it cites.
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2017
Later among the works it cites.
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2018
Later among the works it cites.
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2018
Later among the works it cites.
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2018
Later among the works it cites.
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2018
Later among the works it cites.
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Later among the works it cites.
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Later among the works it cites.
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Later among the works it cites.
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2020
Later among the works it cites.
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2020
Later among the works it cites.