Light-Cone and Diffusive Propagation of Correlations in a Many-Body Dissipative System

We analyze the propagation of correlations after a sudden interaction change in a strongly interacting quantum system in contact with an environment. In particular, we consider an interaction quench in the Bose-Hubbard model, deep within the Mott-insulating phase, under the effect of dephasing. We observe that dissipation effectively speeds up the propagation of single-particle correlations while reducing their coherence. In contrast, for two-point density correlations, the initial ballistic propagation regime gives way to diffusion at intermediate times. Numerical simulations, based on a time-dependent matrix product state algorithm, are supplemented by a quantitatively accurate fermionic quasiparticle approach providing an intuitive description of the initial dynamics in terms of holon and doublon excitations.

Figure 1

Evolution of the real part of $C_{+-}(d,t)$ for various distances following a sudden interaction change from an atomic Mott insulator to $U=40J$ in the presence of an environment with coupling $\hslash \gamma =0.4J$ [the correlations are shifted by $-0.04(d-1)$ to improve readability]. Full blue circles: t-MPS results; full gray line: analytical solution; full green line: envelope of the analytical solution; dashed gray line: envelope of the analytical solution for $\gamma =0$; red circles and triangles: position of the first maximum of $C_{+-}$ for $\hslash \gamma =0.4J$ and 0. Inset: time at which the first maximum of $C_{+-}$ reaches a given distance for various dissipation strengths [obtained within the quasiparticle picture using Eq. (2)].

Figure 2

Evolution of two-point density correlations following a sudden interaction change from an atomic Mott insulator to $U=40J$ for various distances and dissipative strengths [the correlations are shifted by $-0.002(d-2)$]. The large dots mark the times at which the first maximum of $C_{+-}$ reaches a given distance.

Figure 3

Normalized density correlations as a function of distance for various times and two dissipative strengths. The full lines are fits to the function $\exp [-\alpha (d-2)\sqrt{\hslash /(Jt)}]$, $\alpha$ is the only free parameter. The dashed lines are solely guides to the eye.