Real space renormalization group with effective interactions: applications to 2-D spin lattices

M. Hajj (), N. Guihéry, J.-P. Malrieu and B. Bocquillon

The European Physical Journal B: Condensed Matter and Complex Systems, 2004, vol. 41, issue 1, 11-21

Abstract: 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 J 2 /J 1 checkerboard lattice is studied and a location of the phase transition between the Néel phase and the dimer phase is proposed. Copyright Springer-Verlag Berlin/Heidelberg 2004

Date: 2004
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DOI: 10.1140/epjb/e2004-00288-4

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