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Consider the partition function of a classical system in two spatial dimensions, or the Euclidean path integral of a quantum system in two space-time dimensions, both on a lattice.
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Z.-C. Gu, X.-G.Wen Phys. Rev. B 80, 155131 (2009), arXiv:0903.1069
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G. Evenbly, P. Corboz, G. Vidal, Phys. Rev. B 82, 132411 (2010), arXiv:0912.2166
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G. Evenbly and G. Vidal, Phys. Rev. Lett. 115, 180405 (2015), arXiv:1412.0732
2015
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M. Bal, M. M. Rams, V. Zauner, J. Haegeman, F. Verstraete, Matrix product state renormalization
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When applied to the two-dimensional Ising model, tensor network renormalization [ 11 ] was shown to explicitly recover scale invariance at the expected fixed points of the RG flow, including at the critical point. At non-critical fixed-points, TNR recovered the fixed-point tensors previously obtained by Gu and Wen’s tensor entanglement-filtering renormalization (TEFR) [ 9 ]
Cited in the paper.
G. Evenbly, Algorithms for tensor network renormalization
Cited in the paper.
See Supplemental Material for further details on a number of aspects of using tensor network renormalization to implement local scale transformations, which includes Refs. [ 18 , 19 , 20 , 21 ]
Cited in the paper.
D. Gaiotto, private communication
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M. Hauru, G. Evenbly, G. Vidal, Topological conformal defects with tensor networks
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The linear map ℛ t \mathcal{R}_{t} is numerically seen to become approximately (but accurately) independent of t t only after suitably normalizing the original tensors A A (so as to eliminate the non-universal, extensive part of the free energy log ( Z ) \log(Z) , see Ref. [ 17 ] Section E, which would otherwise appear as a t t -dependent multiplicative factor in ℛ t \mathcal{R}_{t} ), and fixing the gauge freedom in the tensor network, as explained in [ 16 ]
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