Currents and Green's functions of impurities out of equilibrium -- results from inchworm Quantum Monte Carlo

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuous-time quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three $t_{2g}$ orbitals of SrVO$_3$ within dynamical mean fi...

We generalize the recently developed diagrammatic Monte Carlo techniques for quantum impurity models from an imaginary time to a Keldysh formalism suitable for real-time and nonequilibrium calculations. Both weak-coupling and strong-coupling based methods are introduced, analysed and applied to the study of transport and relaxation dynamics in interacting quantum dots.

Numerically exact continuous-time Quantum Monte Carlo algorithm for finite fermionic systems with non-local interactions is proposed. The scheme is particularly applicable for general multi-band time-dependent correlations since it does not invoke Hubbard-Stratonovich transformation. The present determinantal grand-canonical method is based on a stochastic series expansion for the partition function in the interaction representation. The results for the Green function and for...

We derive the improved estimators for general interactions and employ these for the continuous-time quantum Monte Carlo method. Using a worm algorithm we show how measuring higher-ordered correlators leads to an improved high-frequency behavior in irreducible quantities such as the one-particle self-energy or the irreducible two-particle vertex for non-density-density interactions. A good knowledge of the asymptotics of the two-particle vertex is essential for calculating non...

A Monte Carlo sampling of diagrammatic corrections to the non-crossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady state properties of nonequilibrium quantum impurity models. This `bold' expansion converges uniformly in time and significantly ameliorates the sign problem that has heretofore limited the power of real-time Monte Carlo approaches to strongly interacting real-time quantum problems. The new approach enables th...

We present a simple, general purpose, quantum Monte-Carlo algorithm for out-of-equilibrium interacting nanoelectronics systems. It allows one to systematically compute the expansion of any physical observable (such as current or density) in powers of the electron-electron interaction coupling constant $U$. It is based on the out-of-equilibrium Keldysh Green's function formalism in real-time and corresponds to evaluating all the Feynman diagrams to a given order $U^n$ (up to $...

We investigate the possibility to assist the numerically ill-posed calculation of spectral properties of interacting quantum systems in thermal equilibrium by extending the imaginary-time simulation to a finite Schwinger-Keldysh contour. The effect of this extension is tested within the standard Maximum Entropy approach to analytic continuation. We find that the inclusion of real-time data improves the resolution of structures at high energy, while the imaginary-time data are...

We present a new continuous time solver for quantum impurity models such as those relevant to dynamical mean field theory. It is based on a stochastic sampling of a perturbation expansion in the impurity-bath hybridization parameter. Comparisons to quantum Monte Carlo and exact diagonalization calculations confirm the accuracy of the new approach, which allows very efficient simulations even at low temperatures and for strong interactions. As examples of the power of the meth...

The inchworm expansion is a promising approach to solving strongly correlated quantum impurity models due to its reduction of the sign problem in real and imaginary time. However, inchworm Monte Carlo is computationally expensive, converging as $1/\sqrt{N}$ where $N$ is the number of samples. We show that the imaginary time integration is amenable to quasi Monte Carlo, with enhanced $1/N$ convergence, by mapping the Sobol low-discrepancy sequence from the hypercube to the sim...

We present a time-linear scaling method to simulate open and correlated quantum systems out of equilibrium. The method inherits from many-body perturbation theory the possibility to choose selectively the most relevant scattering processes in the dynamics, thereby paving the way to the real-time characterization of correlated ultrafast phenomena in quantum transport. The open system dynamics is described in terms of an embedding correlator from which the time-dependent curren...