Statistics of orthogonality catastrophe events in localised disordered lattices

: Cosco F, Borrelli M, Laine EM, Pascazio S, Scardicchio A, Maniscalco S

Publisher: IOP PUBLISHING LTD

: 2018

: New Journal of Physics

: NEW JOURNAL OF PHYSICS

: NEW J PHYS

: ARTN 073041

: 20

: 1

: 11

: 1367-2630

DOI: https://doi.org/10.1088/1367-2630/aad10b

: https://research.utu.fi/converis/portal/detail/Publication/35452613

We address the phenomenon of statistical orthogonality catastrophe in insulating disordered systems. In more detail, we analyse the response of a system of non-interacting fermions to a local perturbation induced by an impurity. By inspecting the overlap between the pre- and post-quench many-body ground states we fully characterise the emergent statistics of orthogonality events as a function of both the impurity position and the coupling strength. We consider two well-known one-dimensional models, namely the Anderson and Aubry-Andre insulators, highlighting the arising differences. Particularly, in the Aubry-Andre model the highly correlated nature of the quasi-periodic potential produces unexpected features in how the orthogonality catastrophe occurs. We provide a quantitative explanation of such features via a simple, effective model. We further discuss the incommensurate ratio approximation and suggest a viable experimental verification in terms of charge transfer statistics and interferometric experiments using quantum probes.

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