Non-local Adiabatic Response of a Localized System to Local Manipulations

TL;DR

This paper reveals that localized systems under slow local perturbations exhibit a non-local response involving conserved quantities over a logarithmic length scale, impacting quantum computation and control in disordered systems.

Contribution

It demonstrates a non-local, beyond linear response effect in localized phases caused by slow local perturbations, a phenomenon not observed in clean insulators.

Findings

Induces a non-local response involving conserved quantities over a logarithmic length scale

Impacts topological quantum computation by showing slow manipulations fail in localized systems

Reveals disorder localized insulators experience a statistical orthogonality catastrophe

Abstract

We examine the response of a system localized by disorder to a time dependent local perturbation which varies smoothly with a characteristic timescale $\tau$. We find that such a perturbation induces a non-local response, involving a rearrangement of conserved quantities over a length scale $\sim \ln \tau$. This effect lies beyond linear response, is absent in undisordered insulators and highlights the remarkable subtlety of localized phases. The effect is common to both single particle and many body localized phases. Our results have implications for numerous fields, including topological quantum computation in quantum Hall systems, quantum control in disordered environments, and time dependent localized systems. For example, they indicate that attempts to braid quasiparticles in quantum Hall systems or Majorana nanowires will surely fail if the manipulations are performed asymptotically slowly, and thus using such platforms for topological quantum computation will require considerable engineering. They also establish that disorder localized insulators suffer from a statistical orthogonality catastrophe.