Exponential Orthogonality Catastrophe in Single-Particle and Many-Body Localized Systems

TL;DR

This paper reveals that localized quantum systems exhibit an exponential decay in wave function overlap after a local quench, contrasting with metallic systems, and discusses its experimental observability.

Contribution

It demonstrates the exponential orthogonality catastrophe in localized systems and shows its persistence with interactions, providing new insights into quantum localization phenomena.

Findings

Exponential decay of wave function overlap with system size in localized systems

Persistence of exponential StOC in many-body localized phases with interactions

Experimental signatures in Ramsey interference and radio-frequency spectroscopy

Abstract

We investigate the statistical orthogonality catastrophe (StOC) in single-particle and many-body localized systems by studying the response of the many-body ground state to a local quench. Using scaling arguments and exact numerical calculations, we establish that the StOC gives rise to a wave function overlap between the pre- and post-quench ground states that has an \emph{exponential} decay with the system size, in sharp contrast to the well-known power law Anderson orthogonality catastrophe in metallic systems. This exponential decay arises from a statistical charge transfer process where a particle can be effectively "transported" to an arbitrary lattice site. In a many-body localized phase, this non-local transport and the associated exponential StOC phenomenon persist in the presence of interactions. We study experimental consequences of the exponential StOC on Loschmidt echo and spectral function, establishing that this phenomenon should be observable in cold atomic experiments through Ramsey interference and radio-frequency spectroscopy.