Topological entanglement properties of disconnected partitions in the Su-Schrieffer-Heeger model

Abstract

We study the disconnected entanglement entropy, SD, of the Su-Schrieffer-Heeger model. SD is a combination of both connected and disconnected bipartite entanglement entropies that removes all area and volume law contributions and is thus only sensitive to the non-local entanglement stored within the ground state manifold. Using analytical and numerical computations, we show that SD behaves like a topological invariant, i.e., it is quantized to either 0 or 2 log(2) in the topologically trivial and non-trivial phases, respectively. These results also hold in the presence of symmetry-preserving disorder. At the second-order phase transition separating the two phases, SD displays a finite-size scaling behavior akin to those of conventional order parameters, that allows us to compute entanglement critical exponents. To corroborate the topological origin of the quantized values of SD, we show how the latter remain quantized after applying unitary time evolution in the form of a quantum quench, a characteristic feature of topological invariants associated with particle-hole symmetry.