Spatio-Temporal Spreading of Correlations in the Bose–Hubbard Model

We have developed a formalism that allows the study of correlations in space and time in the Bose–Hubbard model, both in equilibrium and out of equilibrium. We obtain a two-particle irreducible effective action in the contour-time formalism that allows us to obtain equations of motion for the superfluid order parameter and two-point correlation functions. We use these equations to calculate equilibrium phase diagrams that are significant improvements on mean field theory and apply them to study the spreading of correlations after a quench in the Mott insulator phase. We study the single-particle density matrix and find velocities for the spreading of correlations in one, two and three dimensions. We discuss the prospects of generalizing this approach to study the disordered Bose–Hubbard model.