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

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.

6 pages, 3 figures, published version

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• Nonequilibrium dynamical mean-field theory for bosonic lattice models
• Equilibrium and dynamical phase transitions in fully connected quantum Ising model: Approximate energy eigenstates and critical time
• Mean-field dynamics to negative absolute temperatures in the Bose-Hubbard model
• Transition between vacuum and finite-density states in the infinite-dimensional Bose-Hubbard model with spatially inhomogeneous dissipation