The Anderson--Holstein Model in Two Flavors of the Non--Crossing Approximation

TL;DR

This paper investigates the Anderson-Holstein model using two non-crossing approximation methods to understand electron-phonon interactions' effects on spectral and transport properties in open quantum systems.

Contribution

It compares two non-crossing approximation approaches, highlighting their differences and limitations in modeling electron-phonon interactions in the Anderson-Holstein model.

Findings

The two methods show nontrivial disagreements.

Both approaches have limitations in certain regimes.

The frameworks can serve as starting points for more exact methods.

Abstract

The dynamical interplay between electron-electron interactions and electron-phonon coupling is investigated within the Anderson-Holstein model, a minimal model for open quantum systems that embody these effects. The influence of phonons on spectral and transport properties is explored in equilibrium, for non-equilibrium steady state and for transient dynamics after a quench. Both the particle-hole symmetric and the more generic particle-hole asymmetric cases are studied. The treatment is based on two complementary non-crossing approximations, the first of which is constructed around the weak-coupling limit and the second around the polaron limit. In general, the two methods disagree in nontrivial ways, indicating that more reliable approaches to the problem are needed. The frameworks used here can form the starting point for numerically exact methods based on bold-line continuous-time quantum Monte Carlo algorithms capable of treating open systems simultaneously coupled to multiple fermionic and bosonic baths.