Orthogonality Catastrophe in Dissipative Quantum Many-Body Systems

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.