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)∝t^{θ}e^{-γt}, when the system supports long-range correlations, in a fashion reminiscent of traditional instances of orthogonality catastrophe in condensed matter. An exponential falloff at rate γ 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.