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

### Orazio Scarlatella (Collège de France)

Online seminar — Zoom Meeting ID: 962 2949 3343 — Passcode: ask L. Mazza and D. Petrov —

Markovian quantum many body systems describe a number of experimental platforms relevant for quantum simulations. Their theoretical understanding is hampered by the exponential scaling of their Hilbert space and by their intrinsic nonequilibrium nature, limiting the applicability of many traditional approaches. In this talk I will present an extension of the nonequilibrium Dynamical Mean Field Theory (DMFT) to bosonic Markovian open quantum systems. Within DMFT, a Lindblad master equation describing a lattice of dissipative particles is mapped onto an impurity problem describing a single site of the lattice coupled to a self-consistent environment, which for bosons accounts for fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. I will present a non-perturbative approach to solve this impurity problem, which is tailored for Markovian open quantum systems. As a first application of this DMFT approach, I will discuss the steady-state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. I will show that this model features a normal phase at small hopping and a phase transition towards a non-equilibrium superfluid. Remarkably, this transition occurs as a finite-frequency instability, leading to an oscillating in time order parameter. Then, I will show that DMFT captures hopping-induced dissipative processes, completely missed in Gutzwiller mean-field theory, which crucially determine the properties of the normal phase, including the suppression of local gain and the emergence of a stationary quantum-Zeno regime. I will also argue that these processes compete with coherent hopping processes to determine the phase transition towards the superfluid phase, leading to a large extension of the normal phase due to finite-connectivity.