Revealing strong correlations in higher order transport statistics: a noncrossing approximation approach

Abstract

We present a method for calculating the full counting statistics of a nonequilibrium quantum system based on the propagator noncrossing approximation (NCA). This numerically inexpensive method can provide higher order cumulants for extended parameter regimes, rendering it attractive for a wide variety of purposes. We compare NCA results to Born-Markov quantum master equations (QME) results to show that they can access different physics, and to numerically exact inchworm quantum Monte-Carlo data to assess their validity. As a demonstration of its power, the NCA method is employed to study the impact of correlations on higher order cumulants in the nonequilibrium Anderson impurity model. The four lowest order cumulants are examined, allowing us to establish that correlation effects have a profound influence on the underlying transport distributions. Higher order cumulants are therefore demonstrated to be a proxy for the presence of Kondo correlations in a way that cannot be captured by simple QME methods.

Resolving the nonequilibrium Kondo singlet in energy- and position-space using quantum measurements

“…Our work is based on a noncrossing approximation (NCA), and can therefore be expected to be only qualitatively accurate [59,60,[63][64][65][66]. However, the model can be solved to a numerically exact level of accuracy within Inchworm Monte Carlo methods, and several other methodologies may also be applicable.…”

“…To solve the nonequilibrium impurity problem, we use the propagator flavor of the noncrossing approximation (NCA) [58][59][60]. Variants of the NCA and its extensions have been used to study various aspects of the nonequilibrium Kondo effect [45,46,58,59,[61][62][63]. The method provides qualitatively, though not quantitatively, accurate results at higher temperatures in the Kondo regime, and its regions of applicability have often been explored [59,60,[63][64][65][66].…”

“…Variants of the NCA and its extensions have been used to study various aspects of the nonequilibrium Kondo effect [45,46,58,59,[61][62][63]. The method provides qualitatively, though not quantitatively, accurate results at higher temperatures in the Kondo regime, and its regions of applicability have often been explored [59,60,[63][64][65][66]. However, it cannot be used to systematically examine, e.g., the scaling limit that emerges at low energies, where exact numerical approaches are generally needed.…”