Edwards polaron formation: From 1D to 3D

Employing a self-consistent (optimized) variational diagonalization scheme we investigate the formation of polaronic quasiparticles in a spinless fermion-boson transport model that couples the movement of charge carriers to uctuations and correlations of a background medium. The background is parameterized by bosonic degrees of freedom. The variational fermion-boson Hilbert space is constructed to achieve high accuracy in one to three spatial dimensions with modest computational requirements. To characterize the ground-state properties of the Edwards model in a wide parameter regime, we present exact numerical results for the polaron band dispersion, quasiparticle weight, Drude weight, mass enhancement, and the particle-boson correlations. In the Edwards model transport can be quasi-free, diffusive or boson-assisted in the weakly fermion-boson coupled, fluctuation-dominated or strongly correlated regimes, respectively. Thereby correlated transport is not only assisted but also limited by the bosonic excitations. As a result the Drude weight remains finite even in the limit of very small boson frequencies. For a strongly correlated background closed loops are important, in any dimension, to generate a finite effective particle mass even when the free fermion has an infinite mass.