We study a driven-dissipative Bose-Hubbard model in the presence of two-particle losses and an incoherent single-particle drive on each lattice site, leading to a finite-density stationary state. Using dynamical meanfield theory (DMFT) and an impurity solver based on exact diagonalization of the associated Lindbladian, we investigate the regime of strong two-particle losses. Here a stationary-state quantum Zeno effect emerges, as can be seen in the on-site occupation and spectral function. We show that DMFT captures this effect through its self-consistent bath. We show that, in the deep Zeno regime, the bath structure simplifies, with the occupation of all bath sites except one becoming exponentially suppressed. As a result, an effective dissipative hard-core Bose-Hubbard dimer model emerges, where the auxiliary bath site has single-particle dissipation controlled by the Zeno dissipative scale.
We study a driven-dissipative Bose-Hubbard model in the presence of two-particle losses and an incoherent single-particle drive on each lattice site, leading to a finite-density stationary state. Using dynamical meanfield theory (DMFT) and an impurity solver based on exact diagonalization of the associated Lindbladian, we investigate the regime of strong two-particle losses. Here a stationary-state quantum Zeno effect emerges, as can be seen in the on-site occupation and spectral function. We show that DMFT captures this effect through its self-consistent bath. We show that, in the deep Zeno regime, the bath structure simplifies, with the occupation of all bath sites except one becoming exponentially suppressed. As a result, an effective dissipative hard-core Bose-Hubbard dimer model emerges, where the auxiliary bath site has single-particle dissipation controlled by the Zeno dissipative scale.
A number of experimental platforms relevant for quantum simulations, ranging from arrays of superconducting circuits hosting correlated states of light to ultracold atoms in optical lattices in the presence of controlled dissipative processes. 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 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 fluctuations beyond Gutzwiller mean-field theory due to the finite lattice connectivity. We develop a nonperturbative approach to solve this bosonic impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of noncrossing diagrams. As a first application of our approach, we address the steady state of a driven-dissipative Bose-Hubbard model with two-body losses and incoherent pump. We 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 redistribution of steady-state populations, the suppression of local gain, and the emergence of a stationary quantum-Zeno regime. We argue that these processes compete with coherent hopping to determine the phase transition toward a nonequilibrium superfluid, leading to a strong renormalization of the phase boundary at finite connectivity. We show that this transition occurs as a finite-frequency instability, leading to an oscillating-in-time order parameter, that we connect with a quantum many-body synchronization transition of an array of quantum van der Pol oscillators.
Open quantum many body systems describe several quantum simulators, ranging from arrays of superconducting circuits hosting correlated states of light, to ultracold atoms in optical lattices in presence of controlled dissipative processes. 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 work we extend Dynamical Mean Field Theory (DMFT), a powerful nonperturbative technique developed for strongly correlated quantum many-body systems, to Markovian open quantum systems. Within Open-DMFT, a master equation describing a lattice of bosonic particles is mapped, at large but finite connectivity, onto an impurity problem describing a single site coupled to Markovian and non-Markovian environments, where the latter accounts for quantum fluctuations beyond Gutzwiller mean-field theory. We introduce a new non-perturbative approach to solve the impurity problem, which dresses the impurity, featuring Markovian dissipative channels, with the non-Markovian bath, in a self-consistent scheme based on a resummation of non-crossing diagrams. Finally, we apply our Open-DMFT to solve a driven-dissipative Bose-Hubbard model, which is relevant to current experiments with dissipative ultracold bosons. We show that this model undergoes a dissipative phase transition towards a superfluid phase, which can be equally interpreted as a quantum many-body synchronization transition of an array of quantum van der Pol oscillators. We show how Open-DMFT captures crucial effects due to finite lattice connectivity, such as hopping-induced dissipation and heating, which are completely missed by mean field theories and which lead to a drastic reduction of the broken symmetry phase that we interpret as a desynchronization driven by quantum fluctuations.
Abstract We investigate signatures of a self-trapping transition in the driven-dissipative Bose Hubbard dimer, in presence of incoherent pump and single-particle losses. For fully symmetric couplings the stationary state density matrix is independent of any Hamiltonian parameter, and cannot therefore capture the competition between hopping-induced delocalization and the interaction-dominated self-trapping regime. We focus instead on the exact quantum dynamics of the particle imbalance after the system is prepared in a variety of initial states, and on the frequency-resolved spectral properties of the steady state, as encoded in the single-particle Green’s functions. We find clear signatures of a localization-delocalization crossover as a function of hopping to interaction ratio. We further show that a finite a pump-loss asymmetry restores a delocalization crossover in the steady-state imbalance and leads to a finite intra-dimer dissipation.
We study the self-trapping transition in dissipative double wells using mean-field theory and exact diagonalization. We find that, similar to the conventional interaction-driven transition from oscillatory dynamics to self-trapping, dissipation alone can also induce self-trapping-like localization in one well. The resulting state, although transient and decaying, persists for a substantial time. At the mean-field level, the interaction- and dissipation-driven transitions are discontinuous and continuous, respectively. When interaction and dissipation both are present, their interplay produces three dynamical regimes: (i) at weak interaction, increasing dissipation drives a transition from oscillations to self-trapping; (ii) at moderate interaction, self-trapping at weak dissipation, oscillatory dynamics at intermediate dissipation, and re-entrant self-trapping at strong dissipation; and (iii) at strong interaction, self-trapping persists but is weakened by dissipation. We connect the transition with the Liouvillian spectrum. It is observed that purely dissipation-driven transition coincides with an exceptional point in the spectra, and a peak in the Liouvillian gap, marking the onset of the quantum-Zeno regime. In the presence of interactions, however, the onset of the Zeno regime is shifted to dissipation strengths larger than that required for the self-trapping transition.
This thesis investigates the physics of strongly interacting driven–dissipative bosonic systems in one dimension, combining field-theoretical approaches with various numerical simulation techniques. While weakly interacting condensates are accurately described by a generalized Gross–Pitaevskii equation, the strongly correlated regime of the same microscopic models remains far less understood, particularly out of equilibrium. This thesis aims to bridge this gap by developing controlled quantum-many-body simulations for open systems governed by Lindblad dynamics, as well as investigating the corresponding action under the functional renormalization group.In the first part, we formulate a field-theoretical description of driven–dissipative one-dimen-sional bosons using the Schwinger–Keldysh formalism and the functional renormalization group (fRG).Two models are analyzed: (i) a driven-dissipative condensate whose phase dynamics is expected to exhibit emergent Kardar–Parisi–Zhang (KPZ) behavior, for which we search the emergent KPZ fixed point starting from the bosonic field theory; and (ii) a two-photon–driven system with two-body losses realizing dissipative cat qubits. For the latter, we determine the phase diagram and identify a continuous phase transition between symmetry-broken and symmetric phases, which motivates the construction of an fRG Ansatz capturing this critical behavior.The second part of the thesis focuses on the open system dynamics using exact diagonalization and tensor-network methods. For the Bose–Hubbard model with incoherent pump and loss, we characterize the steady state, and study spectral functions across the full parameter space. We show that key ground-state features are absent under dissipation, while the high-temperature unitary spectrum captures aspects of the open-system dynamics. In an extended model with additional two-body and non-local losses, we establish the semi-classical emergence of KPZ scaling and extract the KPZ dynamical exponent from the spectral function. A finite-size analysis exposes the current limitations of the tensor-network methods for reaching the high occupancy regime in the full quantum evolution.Finally, a last project develops a two-loop perturbative RG analysis of a spin-1 chain at its continuous symmetry breaking quantum critical point, revealing critical exponents distinct from the Ising universality class.Together, these results advance the understanding of strongly interacting open quantum systems, elucidating their symmetries, effective field theories, and dynamical properties, and outlining key directions for future theoretical and numerical work.
We study a dissipative version of the Anderson Impurity model, where an interacting impurity is coupled to a fermionic reservoir and exposed to Markovian dissipation in the form of two-body losses. Using a self-consistent hybridization expansion based on the Non-Crossing Approximation (NCA) we compute the dynamics of the impurity, its steady-state and spectral function. We show that the interplay between strong Coulomb repulsion and correlated dissipation gives rise to robust signatures of Kondo physics both at weak and strong losses. These include a strongly suppressed spin relaxation rate, displaying a characteristic Kondo-Zeno crossover and a spectral function where doublon band is quickly destroyed by dissipation while the coherent Kondo peak remains visible for weak losses, then disappears at intermediate values and finally re-emerge as the system enters in the Kondo-Zeno regime. As compared to the case of single particle losses we show that two-body dissipation protects Kondo physics. The picture obtained with NCA is confirmed by numerical simulations of exact dynamics on finite-size chains. We interpret these results using a dissipative Schrieffer-Wolff transformation, which leads to an effective Kondo model with residual impurity-bath losses which are suppressed by strong correlations or strong losses.