Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems

Understand

Open quantum many body systems describe a number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits to ultracold atoms in optical lattices.

• Their theoretical understanding is hampered by their large Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches.
• In this work we extend the nonequilibrium bosonic Dynamical Mean Field Theory (DMFT) to Markovian open quantum systems.
• Within DMFT, a Lindblad master equation describing a lattice of dissipative bosonic particles is mapped onto an impurity problem describing a single site embedded in its Markovian environment and coupled to a self-consistent field and to a non-Markovian bath, where the latter accounts for finite lattice connectivity corrections beyond Gutzwiller mean-field theory.