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

TL;DR

This paper investigates the disconnected entanglement entropy in the Su-Schrieffer-Heeger model, demonstrating its role as a topological invariant that distinguishes trivial and non-trivial phases, even under disorder and dynamical evolution.

Contribution

It introduces and analyzes the disconnected entanglement entropy as a topological invariant in the SSH model, including its behavior at phase transitions and under quantum quenches.

Findings

$S^D$ is quantized to 0 or 2 log(2) in trivial and topological phases.

$S^D$ remains quantized under symmetry-preserving disorder.

$S^D$ exhibits critical scaling at phase transitions.

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.