Comparison of non-crossing perturbative approach and generalized projection method for strongly coupled spin-fermion systems at low doping

We analyze the two-dimensional spin-fermion model in the strong coupling regime relevant to underdoped cuprates. We recall the set of general sumrules that relate moments of spectral density and the imaginary part of fermion self-energy with static correlation functions. We show that two-pole approximation of projection method satisfies the sumrules for first four moments of spectral density and gives an exact upper bound for quasiparticle energy near the band bottom. We prove that non-crossing approximation that is often made in perturbative consideration of the model violates the sumrule for third moment of spectral density. This leads to wrong position of lowest quasiparticle band. On the other hand, the projection method is inadequate in weak coupling limit because of approximate treatment of kinetic energy term. We propose a generalization of projection method that overcomes this default and give the fermion self-energy that correctly behaves both in weak and strong coupling limits.Comment: 9 pages, 4 EPS figures, RevTe

Spin polaron damping in the spin-fermion model for cuprate superconductors

A self-consistent, spin rotational invariant Green's function procedure has been developed to calculate the spectral function of carrier excitations in the spin-fermion model for the CuO2 plane. We start from the mean field description of a spin polaron in the Mori-Zwanzig projection method. In order to determine the spin polaron lifetime in the self-consistent Born approximation, the self-energy is expressed by an irreducible Green's function. Both, spin polaron and bare hole spectral functions are calculated. The numerical results show a well pronounced quasiparticle peak near the bottom of the dispersion at (pi/2,pi/2), the absence of the quasiparticle at the Gamma-point, a rather large damping away from the minimum and an asymmetry of the spectral function with respect to the antiferromagnetic Brillouin zone. These findings are in qualitative agreement with photoemission data for undoped cuprates. The direct oxygen-oxygen hopping is responsible for a more isotropic minimum at (pi/2,pi/2).Comment: 18 pages, 13 figure