Real space renormalization group with effective interactions: applications to 2-D spin lattices
Laboratoire de Physique Quantique, IRSAMC/UMR5626, Université Paul Sabatier, 118 route de Narbonne, 31062 Toulouse Cedex 4, France
Corresponding author: a firstname.lastname@example.org
Revised: 11 June 2004
Published online: 30 September 2004
The Bloch's theory of effective Hamiltonians has been used to improve the Real Space Renormalization Group approach. The effective interactions between elementary blocks of a periodic lattice can be extracted from the knowledge of the spectrum of the dimers or trimers of blocks. The potentialities of the method are illustrated on a series of quasi 1-D and 2-D problems. The spin gap of two-leg ladders is calculated and an estimate of the impact of ferromagnetic couplings between two-leg ladders on the gap is presented. The method satisfactorily identifies the phase transitions in the 1/5-depleted square lattice as well as in the spin-frustrated Shastry-Sutherland lattice. The checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed.
PACS: 71.10.-W – Theories and models of many-electron systems / 71.15.Nc – Total energy and cohesive energy calculations / 75.10.-b – General theory and models of magnetic ordering
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2004