Momentum average approximation for models with boson-modulated hopping: Role of closed loops in the dynamical generation of a finite quasiparticle mass

TL;DR

This paper extends the momentum average approximation to models with boson-modulated hopping, revealing how closed loops like Trugman loops contribute to finite quasiparticle mass in polaron systems.

Contribution

The authors generalize the momentum average approximation to include momentum-dependent fermion-boson interactions and demonstrate its effectiveness in analyzing polaron properties in higher dimensions.

Findings

Validated the approximation against exact diagonalization in 1D.

Calculated polaron dispersion and quasiparticle weight in 2D.

Showed the role of Trugman loops in generating finite effective mass.

Abstract

We generalize the momentum average approximation to study the properties of single polarons in models with boson affected hopping, where the fermion-boson scattering depends explicitly on both the fermion's and the boson's momentum. As a specific example, we investigate the Edwards fermion-boson model in both one and two dimensions. In one dimension, this allows us to compare our results with exact diagonalization results, to validate the accuracy of our approximation. The generalization to two-dimensional lattices allows us to calculate the polaron's quasiparticle weight and dispersion throughout the Brillouin zone and to demonstrate the importance of Trugman loops in generating a finite effective mass even when the free fermion has an infinite mass.