A Green's function decoupling scheme for the Edwards fermion-boson model

TL;DR

This paper develops an analytical Green's function decoupling scheme for the Edwards fermion-boson model, enabling the study of ground state and spectral properties across different dimensions and fermion densities.

Contribution

It introduces a new analytical decoupling scheme for the Green's function applicable to arbitrary densities and dimensions in the Edwards fermion-boson model.

Findings

Good agreement with numerical DMRG results in 1D

Provides insights into ground state properties at various fillings

Paves the way for extending analysis to 2D and 3D

Abstract

Holes in a Mott insulator are represented by spinless fermions in the fermion-boson model introduced by Edwards. Although the physically interesting regime is for low to moderate fermion density the model has interesting properties over the whole density range. It has previously been studied at half-filling in the one-dimensional (1D) case by numerical methods, in particular exact diagonalization and density matrix renormalization group (DMRG). In the present study the one-particle Green's function is calculated analytically by means of a decoupling scheme for the equations of motion, valid for arbitrary density in 1D, 2D and 3D with fairly large boson energy and zero boson relaxation parameter. The Green's function is used to compute some ground state properties, and the one-fermion spectral function, for fermion densities n=0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numerical results obtained by DMRG and dynamical DMRG and new light is shed on the nature of the ground state at different fillings. The Green's function approximation is sufficiently successful in 1D to justify future application to the 2D and 3D cases.