A Green’s function decoupling scheme for the Edwards fermion–boson model

Abstract

Holes in a Mott insulator are represented by spinless fermions in the fermion–boson modelintroduced by Edwards. Although the physically interesting regime is for low to moderatefermion density, the model has interesting properties over the whole density range. Ithas previously been studied at half-filling in the one-dimensional (1D) case bynumerical methods, in particular using exact diagonalization and the density matrixrenormalization group (DMRG). In the present study the one-particle Green’s function iscalculated 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 andzero boson relaxation parameter. The Green’s function is used to compute someground state properties, and the one-fermion spectral function, for fermion densitiesn = 0.1, 0.5 and 0.9 in the 1D case. The results are generally in good agreement with numericalresults obtained using the DMRG and dynamical DMRG, and new light is shed on thenature of the ground state at different fillings. The Green’s function approximationis sufficiently successful in 1D to justify future application to the 2D and 3Dcases.