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

We study the disconnected entanglement entropy, S-D, of the Su-Schrieffer-Heeger model. S-D 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 S-D 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, S-D displays a finitesize 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 S-D, 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. (C) Copyright T. Micallo et al. This work is licensed under the Creative Commons Attribution 4.0 International License. Published by the SciPost Foundation.