Probe of locality in disordered systems

Can one say anything about the transfer of quantum information by measuring
only a simple, single-site observable, but in two similar systems? Using
local density correlation functions for a one-dimensional spin chain, we
introduce a correlation function difference (CFD) which compares
correlations on a given site between a full system of size L and its
restriction to ℓ<L sites [1]. We show that CFD provides useful information
on transfer of information in quantum many-body systems by considering the
examples of ergodic, Anderson, and many-body localized regimes in
disordered XXZ spin chain. In the ergodic phase, we find that the
propagation of CFD is asymptotically faster than the spin transport but
slower than the ballistic propagation implied by the Lieb-Robinson bound.
In contrast, in the localized cases, we unravel an exponentially slow
relaxation of CFD. Connections between CFD and other observables detecting
non-local correlations in the system are discussed.

[1] T. Szołdra, P. Sierant, M. Lewenstein, J. Zakrzewski, Phys. Rev. B 107,
054204 (2023)

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