Rigorous mean-field dynamics of lattice bosons: Quenches from the Mott insulator

TL;DR

This paper rigorously derives mean-field dynamics for lattice bosons, revealing a dynamical critical point that determines the stability of the Mott insulator versus superfluid states after interaction quenches.

Contribution

It provides a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons and identifies a dynamical critical interaction affecting stability after quenches.

Findings

Existence of a dynamical critical interaction $U_d$

Mott insulator stability depends on $U_f$ relative to $U_d$

Mean-field dynamics is exact on fully connected lattices

Abstract

We provide a rigorous derivation of Gutzwiller mean-field dynamics for lattice bosons, showing that it is exact on fully connected lattices. We apply this formalism to quenches in the interaction parameter from the Mott insulator to the superfluid state. Although within mean-field the Mott insulator is a steady state, we show that a dynamical critical interaction $U_d$ exists, such that for final interaction parameter $U_f>U_d$ the Mott insulator is exponentially unstable towards emerging long-range superfluid order, whereas for $U_f<U_d$ the Mott insulating state is stable. We discuss the implications of this prediction for finite-dimensional systems.