Renormalizationgroupinspired neural networks for computing topological invariants
Abstract
We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its twodimensional realspace Hamiltonian. Furthermore, we describe a "renormalizationgroup" (RG) network, an ANN which converts a Hamiltonian on a large lattice to another on a small lattice while preserving the invariant. By iteratively applying the RG network to a "base" network that computes the Chern number of a small lattice of set size, we are able to process larger lattices without retraining the system. We therefore show that it is possible to compute realspace topological invariants for systems larger than those on which the network was trained. This opens the door for computation times significantly faster and more scalable than previous methods.
 Publication:

Physical Review B
 Pub Date:
 May 2022
 DOI:
 10.1103/PhysRevB.105.205139
 arXiv:
 arXiv:2202.07669
 Bibcode:
 2022PhRvB.105t5139M
 Keywords:

 Condensed Matter  Disordered Systems and Neural Networks;
 Condensed Matter  Mesoscale and Nanoscale Physics
 EPrint:
 5+5 pages, 3+4 figures