Dynamical Mean-Field Theory for Markovian Lattice Models

Orazio Scarlatella, Rosario Fazio, Aashish Clerk and Marco Schirò

Several experimental platforms, such as superconducting circuits or ultracold atomic in optical lattices, nowadays allow to probe many-body physics in unprecedented regimes, such as in non-equilibrium conditions resulting from controlled dissipation and driving, but theoretical techniques for describing those regimes are limited. In this work [1], we introduce an extension of the nonequilibrium dynamical mean-field theory (DMFT) for bosonic lattice models described by Markovian master equations. DMFT maps these lattice problems onto a problem of a single site coupled to a classical field and to a non-interacting bath, accounting for leading corrections to Gutzwiller mean-field theory due to finite dimensionality. Our approach relies on a new method for solving the effective single-site problem based on a non-crossing approximation in the coupling to the DMFT bath, going beyond standard Born-Markov approximations [2]. We then discuss an application to a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump, computing its steady-state properties. DMFT captures hopping-induced processes that are completely missed by Gutzwiller mean-field theory, which are crucial to obtain the correct stationary-state, such as to describe its quantum-Zeno behaviour when the losses are strong, or to predict the critical hopping for a phase transition between an incoherent phase and a coherent, limit-cycle phase. [1] O. Scarlatella, A. A. Clerk, R. Fazio, and M. Schiró, Dynamical Mean-Field Theory for Markovian Open Quantum Many-Body Systems, Phys. Rev. X 11, 031018 (2021). [2] O. Scarlatella and M. Schiro, Self-Consistent Dynamical Maps for Open Quantum Systems, arXiv:2107.05553.