Edwards polaron formation : From one to three dimension

TL;DR

This paper investigates polaron formation in a spinless fermion-boson model across one to three dimensions using a variational diagonalization approach, revealing how background correlations influence transport properties.

Contribution

It introduces a high-accuracy variational method for analyzing polaron properties in multiple dimensions within the Edwards model, highlighting the role of bosonic excitations in transport.

Findings

Transport regimes vary from quasifree to boson-assisted depending on coupling strength.

Finite Drude weight persists even at low boson frequencies.

Closed loops are crucial for finite effective mass in strongly correlated backgrounds.

Abstract

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 fluctuations 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 the single-particle sector, we present exact numerical results for the polaron band dispersion, quasiparticle weight, Drude weight, mass enhancement, and the particle-boson correlations in a wide parameter regime. In the Edwards model, transport will be quasifree, 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.