  We present an analog of the phenomenon of orthogonality catastrophe in
quantum many body systems subject to a local dissipative impurity. We show that
the fidelity $F(t)$, giving a measure for distance of the time-evolved state
from the initial one, displays a universal scaling form $F(t)\propto t^\theta
e^{-\gamma t}$, when the system supports long range correlations, in a fashion
reminiscent of traditional instances of orthogonality catastrophe in condensed
matter. An exponential fall-off at rate $\gamma$ signals the onset of
environmental decoherence, which is critically slowed down by the additional
algebraic contribution to the fidelity. This picture is derived within a second
order cumulant expansion suited for Liouvillian dynamics, and substantiated for
the one-dimensional transverse field quantum Ising model subject to a local
dephasing jump operator, as well as for XY and XX quantum spin chains, and for
the two dimensional Bose gas deep in the superfluid phase with local particle
heating. Our results hint that local sources of dissipation can be used to
inspect real-time correlations and to induce a delay of decoherence in open
quantum many body systems.
