Diagrammatic Monte Carlo for real-time propagation

Sam Azadi, Arkadiy Davydov, Evgeny Kozik

Jia Li, Markus Wallerberger, Emanuel Gull

Riccardo Rossi

J. Vučičević, P. Stipsić, Michel Ferrero

The authors find an analytical solution to the imaginary time integrals that arise in quantum many-body perturbation theory, and use it to investigate the two-dimensional Hubbard model with diagrammatic Monte Carlo algorithms.

Fedor Šimkovic, Michel Ferrero

The computation of determinants plays a central role in diagrammatic Monte Carlo algorithms for strongly correlated systems. The evaluation of large numbers of determinants can often be the limiting computational factor determining the number of attainable diagrammatic expansion orders. In this work we build on the algorithm presented in [K. Griffin and M. J. Tsatsomeros, Principal minors, part i: A method for computing all the principal minors of a matrix, Linear Algebra Appl. 419, 107 (2006)] which computes all principal minors of a matrix in $O({2}^{n})$ operations. We present multiple generalizations of the algorithm to the efficient evaluation of certain subsets of all principal minors with immediate applications to connected determinant diagrammatic Monte Carlo within the normal and symmetry-broken phases as well as continuous-time quantum Monte Carlo. Additionally, we improve the asymptotic scaling of diagrammatic Monte Carlo formulated in real time to $O({2}^{n})$ and report speedups of up to a factor 25 at computationally realistic expansion orders. We further show that all permanent principal minors, corresponding to sums of bosonic Feynman diagrams, can be computed in $O({3}^{n})$, thus encouraging the investigation of bosonic and mixed systems by means of diagrammatic Monte Carlo.

Marco Schirò, Michele Fabrizio

We propose a numerically exact approach to nonequilibrium real-time dynamics that is applicable to quantum impurity models coupled to biased noninteracting leads, such as those relevant to quantum transport in nanoscale 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 noninteracting resonant-level model and, as a first nontrivial application, we study zero-temperature nonequilibrium transport through a vibrating molecule.