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A renormalization group flow of Hamiltonians for two-dimensional classical partition functions is constructed using tensor networks.
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Note that by working with symmetric tensor networks, we can also extract CFT data of non-local fields if we modify Eq. ( 3
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Y.-X. Wang and Y.-J. Zhang, IEEE Transactions on Knowledge and Data Engineering 25
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“[…] the more recent tensor-style work often employs indices which are summed over hundreds of values, each representing a sum of configurations of multiple spinlike variables. All these indices are generated and picked by the computer. The analyst does not and cannot keep track of the meaning of all these variables. Therefore, even if a fixed point were generated, it would not be very meaningful to the analyst. In fact, the literature does not seem to contain much information about the values and consequences of fixed points for the new style of renormalization” Efrati et al. 2014
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E. Efrati, Z. Wang, A. Kolan, and L. P. Kadanoff, Reviews of Modern Physics 86
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K. Huang, N. D. Sidiropoulos, and A. Swami, IEEE Transactions on Signal Processing 62
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2017
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See Appendices for details on nonnegative matrix factorization, numerical implementations, entanglement filtering, symmetries, approximate scale invariance, and extracting conformal data from tensor networks, which includes Refs. Gillis 2012 ; Donoho and Stodden 2004 ; Huang et al. 2014 ; Vavasis 2010 ; Seung and Lee 1999 ; Wang and Zhang 2012 ; Gillis 2014 ; Boutsidis and Gallopoulos 2008 ; Knight 2008 ; Pérez-García et al. 2008 ; Cirac et al. 2017
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Note that all these boundary tensor networks are but different low-rank tensor network approximations of the leading eigenvector of the transfer matrix written as a matrix product operator (MPO) Haegeman and Verstraete 2017
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N. Bultinck, M. Mariën, D. Williamson, M. Şahinoğlu, J. Haegeman, and F. Verstraete, Annals of Physics 378
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J. Cirac, D. Pérez-García, N. Schuch, and F. Verstraete, Annals of Physics 378
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