https://doi.org/10.1140/epjb/e2004-00288-4
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 alhajj@irsamc.ups-tlse.fr
Received:
1
March
2004
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
