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

Abstract

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 as 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 system-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 $S^D$, 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.

20 pages, 9 figures. Submission to SciPost v2: -added a section elaborating on why $S^D$ is invariant after a quench, and a section why the conclusion of the paper extend to the whole BDI class. -added references -now 25 pages, 11 figures

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• Topological quantum interference in a pumped Su-Schrieffer-Heeger lattice
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• Quench-Probe Setup as Analyzer of Fractionalized Entanglement Spreading
• Topological squashed entanglement: nonlocal order parameter for one-dimensional topological superconductors
• Emergence of long-range entanglement and odd-even effect in periodic generalized quantum cluster models
• Resource complexity of Symmetry Protected Topological phases
• Detecting entanglement with transport measurement in weakly interacting and fluctuating systems