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arXiv · 2202.07669

Renormalization-group-inspired neural networks for computing topological invariants

Gilad Margalit·Omri Lesser·T. Pereg-Barnea·Yuval Oreg
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Abstract

We show that artificial neural networks (ANNs) can, to high accuracy, determine the topological invariant of a disordered system given its two-dimensional real-space Hamiltonian. Furthermore, we describe a "renormalization-group" (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 re-training the system. We therefore show that it is possible to compute real-space 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.

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BibTeXRIS

Gilad Margalit, Omri Lesser, T. Pereg-Barnea, Yuval Oreg. 2022-02-15. Renormalization-group-inspired neural networks for computing topological invariants. https://doi.org/10.1103/physrevb.105.205139

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