https://doi.org/10.1140/epjb/e2013-30894-8
Regular Article
Long-wavelength spin-effective actions for the infinite U Hubbard model
1 Instituto de Física, Universidad
Federal de Goiás, P.B.131, Campus
II, 74001-970
Goiânia, GO, Brazil
2 International Institute of Physics,
Universidad Federal Rio Grande do Norte, 59072-970
Natal, RN, Brazil
a
e-mail: braghin@if.ufg.br
Received:
2
October
2012
Received in final form:
12
December
2012
Published online:
27
March
2013
The derivation of spin-effective actions is envisaged for the Hubbard model with infinite Coulomb repulsion for a very low concentration of holes with a slave fermion representation for electronic operators. For that, spinless charge variables (vacancies or holes) are integrated out and the resulting effective action at finite temperature is expanded up to the fourth order in the hopping term as proposed in reference [F.L. Braghin, A. Ferraz, E.A. Kochetov, Phys. Rev. B 78, 115109 (2008)] and, in a square lattice, the fourth order term is shown to have the structure of an extended gauge invariant J-Q model for localized spins. Two cases for which the resulting model is non trivial are analysed and they correspond basically to (1) holes hopping between two sub-lattices and (2) a time-dependent solution for the spinon variables in the square lattice. Whereas the first of these cases yields, at the leading order, an effective antiferromagnetic Heisenberg coupling for localized spins and the second one may lead either to ferromagnetic or antiferromagnetic effective coupling. In the second case, the ordering should appear rather in finite size domains and, although charge variables were integrated out, a subtle imbalance between charge degrees of freedom and spins should be at work.
Key words: Solid State and Materials
© EDP Sciences, Società Italiana di Fisica and Springer-Verlag, 2013