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

TL;DR

This paper compares the non-crossing perturbative approach and a generalized projection method for strongly coupled spin-fermion systems, highlighting the projection method's advantages in satisfying sumrules and accurately predicting quasiparticle energies.

Contribution

It introduces a generalized projection method that accurately captures spectral properties in both weak and strong coupling regimes for spin-fermion models.

Findings

Projection method satisfies sumrules for spectral moments.

Non-crossing approximation violates sumrules, leading to incorrect quasiparticle energies.

The generalized projection method performs well in both coupling limits.

Abstract

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.