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

### Submission summary

 As Contributors: Marcello Dalmonte · Pierre Fromholz Arxiv Link: https://arxiv.org/abs/2006.15026v1 (pdf) Date submitted: 2020-07-03 02:00 Submitted by: Fromholz, Pierre Submitted to: SciPost Physics Core Discipline: Physics Subject area: Condensed Matter Physics - Theory Approaches: Theoretical, Computational, Phenomenological

### 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.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 2006.15026v1 on 3 July 2020

## Reports on this Submission

### Report

The authors study the disconnected entanglement entropy in the SSH chain. Their results are in agreement with the well-known phase digram consisting of a phase with edge modes and one without (for the open chain). Thus I do not see anything that is not expected right from the outset. I rather view the manuscript as a case study of the disconnected entanglement entropy in another model. Thus I conclude that the SciPost Physics Core expectations are not met.

More generally I am also unsure whether the results really show that the studied disconnected entanglement entropy picks up information about the topological properties of the system. My problem with this is that the SSH chain doesn't have the same topological properties as, say, the Kitaev chain (which was already studied in Ref. 28). True, one of the phases of the SSH chain possesses edge modes, but these do not show the same degree of protection against local perturbations as in the Kitaev chain. Thus I do not think that from the results one can draw conclusions on topological properties in generality.

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