Renormalization-group-inspired neural networks for computing topological invariants

TL;DR

This paper introduces neural networks inspired by renormalization-group techniques that accurately compute topological invariants of large disordered systems efficiently, enabling scalable analysis beyond training sizes.

Contribution

The authors develop a renormalization-group-inspired neural network that preserves topological invariants while reducing system size, allowing scalable computation of invariants for larger systems without retraining.

Findings

Neural networks can accurately determine topological invariants from real-space Hamiltonians.

The RG network enables processing larger lattices efficiently by iterative size reduction.

The method significantly speeds up computation of topological invariants for large disordered systems.

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.