Renormalization of tensor networks using graphindependent local truncations
Abstract
We introduce an efficient algorithm for reducing bond dimensions in an arbitrary tensor network without changing its geometry. The method is based on a quantitative understanding of local correlations in a network. Together with a tensor network coarsegraining algorithm, it yields a proper renormalization group (RG) flow. Compared to existing methods, the advantages of our algorithm are its low computational cost, simplicity of implementation, and applicability to any network. We benchmark it by evaluating physical observables for the twodimensional classical Ising model and find accuracy comparable with the best existing tensor network methods. Because of its graph independence, our algorithm is an excellent candidate for implementation of realspace RG in higher dimensions. We discuss some of the details and the remaining challenges in three dimensions. Source code for our algorithm is freely available.
 Publication:

Physical Review B
 Pub Date:
 January 2018
 DOI:
 10.1103/PhysRevB.97.045111
 arXiv:
 arXiv:1709.07460
 Bibcode:
 2018PhRvB..97d5111H
 Keywords:

 Condensed Matter  Strongly Correlated Electrons;
 Condensed Matter  Statistical Mechanics;
 High Energy Physics  Theory;
 Quantum Physics
 EPrint:
 14 + 6 pages, 112 figures, source code in ancillary files