A spin-fermion model relevant for the description of cuprates ladders is studied in a path integral formalism, where, after integrating out the fermions, an effective action for the spins in term of a Fermi-determinant results. The determinant can be evaluated in the long-wavelength, low-frequency limit to all orders in the coupling constant, leading to a non-linear sigma model with doping dependent coupling constants. An explicit evaluation shows, that the spin-gap diminishes upon doping as opposed to previous mean-field treatments.
@article{arxiv.cond-mat/0207038,
title = {Doping dependence of the spin gap in a 2-leg ladder},
author = {L. Campos Venuti and A. Muramatsu},
journal= {arXiv preprint arXiv:cond-mat/0207038},
year = {2009}
}