Tensors.net

Example codes: TNR 

Please look at the readme page if you have not done so already. Here we present an implementation of tensor network renormalization (TNR) algorithm which can be applied to contract the partition function of a 2D classical statistical mechanics model or the path-integral of a 1D quantum lattice model. This implementation is largely similar to the example TRG code, but includes the extra disentangling step. We include some of the refinements of TNR discussed in the algorithms manuscript and also use implicit disentangling. The code produces a binary MERA defined from disentanglers u and isometries w as discussed in this manuscript. Two versions of the code are included, where the second version implements the gauge fixing steps necessary to produce a manifestly scale-invariant RG flow for critical systems, thus can be used to compute conformal data.

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Isometries q are chosen to maximize the norm of the C tensor defined below, while isometries v and w are chosen to maximize the norm of the coarse-grained A' tensor defined below. Tensors y, u and s are optimized as to maximize the fidelity between networks T and T' defined below. We assume, for simplicity, that the initial network contains only real coefficients and is symmetric under reflections on both the horizontal and vertical axes.  

• Computational cost: O(χ^6)​

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• Exploits (horizontal and vertical) spatial reflection symmetries

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• Each coarse-graining step involves isometries q, y, w, v and a disentangler u, as well as the implicit disentangler s