RQMP Research Seminar

Renormalization-Group-Inspired Neural Networks for Computing Topological Invariants

Omri Lesser

Weizmann Institute of Science

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. Our ANN is therefore made of two parts. The RG network which is trained to compress the system from large to small and another which is trained to compute the topological invariant on a disordered small sample. By iteratively applying the RG network, we are able to compress 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.