Marcel Goihl, Christian Krumnow, Marek Gluza, Jens Eisert, Nicolas Tarantino
SciPost Phys. 6, 072 (2019) ·
published 21 June 2019
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· pdf
Spin chains with symmetry-protected edge zero modes can be seen as
prototypical systems for exploring topological signatures in quantum systems.
These are useful for robustly encoding quantum information. However in an
experimental realization of such a system, spurious interactions may cause the
edge zero modes to delocalize. To stabilize against this influence beyond
simply increasing the bulk gap, it has been proposed to harness suitable
notions of disorder. Equipped with numerical tools for constructing locally
conserved operators that we introduce, we comprehensively explore the interplay
of local interactions and disorder on localized edge modes in the XZX cluster
Hamiltonian. This puts us in a position to challenge the narrative that
disorder necessarily stabilizes topological order. Contrary to heuristic
reasoning, we find that disorder has no effect on the edge modes in the
Anderson localized regime. Moreover, disorder helps localize only a subset of
edge modes in the many-body interacting regime. We identify one edge mode
operator that behaves as if subjected to a non-interacting perturbation, i.e.,
shows no disorder dependence. This implies that in finite systems, edge mode
operators effectively delocalize at distinct interaction strengths. In essence,
our findings suggest that the ability to identify and control the best
localized edge mode trumps any gains from introducing disorder.
Mr Goihl: "Dear reviewer, Dear readers, ..."
in Submission on Edge mode locality in perturbed symmetry protected topological order by Marcel Goihl, Christian Krumnow, Marek Gluza, Jens Eisert, Nicolas Tarantino