A renormalized excitonic method in terms of block excitations. Application to spin lattices

Abstract

Dividing the lattice into blocks with singlet ground state and knowing the exact low energy spectrum of the blocks and of dimers (or trimers) of blocks, it is possible to approach the lowest part of the lattice spectrum through an excitonic type effective model. The potentialities of the method are illustrated on the 1-D frustrated chain and the 1/5-depleted square and the plaquette 2-D lattices. The method correctly locates the phase transitions between gapped and non-gapped phases.