Deep learning for disordered topological insulators through their entanglement spectrum

Abstract

Calculation of topological invariants for crystalline systems is well understood in reciprocal space, allowing for the topological classification of a wide spectrum of materials. In this work, we present a technique based on the entanglement spectrum, which can be used to identify the hidden topology of systems without translational invariance. By training a neural network to distinguish between trivial and topological phases using the entanglement spectrum obtained from crystalline or weakly disordered phases, we can predict the topological phase diagram for generic disordered systems. This approach becomes particularly useful for gapless systems, while providing a computational speed-up compared to the commonly used Wilson loop technique for gapful situations. Our methodology is illustrated in two-dimensional models based on the Wilson-Dirac lattice Hamiltonian.