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

We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracti...

We present real-time inchworm quantum Monte Carlo results for single-site dynamical mean field theory on an infinite coordination number Bethe lattice. Our numerically exact results are obtained on the L-shaped Keldysh contour and, being evaluated in real-time, avoid the analytic continuation issues typically encountered in Monte Carlo calculations. Our results show that inchworm Monte Carlo methods have now reached a state where they can be used as dynamical mean field impur...

We present a numerically exact Inchworm Monte Carlo method for equilibrium multiorbital quantum impurity problems with general interactions and hybridizations. We show that the method, originally developed to overcome the dynamical sign problem in certain real-time propagation problems, can also overcome the sign problem as a function of temperature for equilibrium quantum impurity models. This is shown in several cases where the current method of choice, the continuous-time ...

We present a method for the calculation of dynamical correlation functions of quantum impurity systems out of equilibrium using Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain and embeds the recently derived algorithm for equilibrium spectral functions. Our method fulfills the spectral weight conserving sum-rule exactly by construction. A local Coulomb repulsion $U>0$ is switched on at $t=0$, and the asymptotic st...

We present optimized implementations of the weak-coupling continuous-time Monte Carlo method defined for nonequilibrium problems on the Keldysh contour. We describe and compare two methods of preparing the system before beginning the real-time calculation: the "interaction quench" and the "voltage quench", which are found to be suitable for large and small voltage biasses, respectively. We also discuss technical optimizations which increase the efficiency of the real-time mea...

We present a quantum Monte-Carlo algorithm for computing the perturbative expansion in power of the coupling constant $U$ of the out-of-equilibrium Green's functions of interacting Hamiltonians of fermions. The algorithm extends the one presented in Phys. Rev. B 91 245154 (2015), and inherits its main property: it can reach the infinite time (steady state) limit since the computational cost to compute order $U^n$ is uniform versus time; the computing time increases as $2^n$. ...

We extend the recently developed real-time Diagrammatic Monte Carlo method, in its hybridization expansion formulation, to the full Kadanoff-Baym-Keldysh contour. This allows us to study real-time dynamics in correlated impurity models starting from an arbitrary, even interacting, initial density matrix. As a proof of concept we apply the algorithm to study the non equilibrium dynamics after a local quantum quench in the Anderson Impurity Model. Being a completely general app...

Multi-orbital quantum impurity models with general interaction and hybridization terms appear in a wide range of applications including embedding, quantum transport, and nanoscience. However, most quantum impurity solvers are restricted to a few impurity orbitals, discretized baths, diagonal hybridizations, or density-density interactions. Here, we generalize the inchworm quantum Monte Carlo method to the interaction expansion and explore its application to typical single- an...

We propose a novel approach to nonequilibrium real-time dynamics of quantum impurities models coupled to biased non-interacting leads, such as those relevant to quantum transport in nanoscale molecular devices. The method is based on a Diagrammatic Monte Carlo sampling of the real-time perturbation theory along the Keldysh contour. We benchmark the method on a non-interacting resonant level model and, as a first non-trivial application, we study zero temperature non-equilibri...

We present a novel technique for the calculation of dynamical correlation functions of quantum impurity systems in equilibrium with Wilson's numerical renormalization group. Our formulation is based on a complete basis set of the Wilson chain. In contrast to all previous methods, it does not suffer from overcounting of excitation. By construction, it always fulfills sum rules for spectral functions. Furthermore, it accurately reproduces local thermodynamic expectation values,...