Real space renormalization group approach to the two-dimensional antiferromagnetic Heisenberg model (I) – The singlet triplet gap
Physics Department, University of Wuppertal, 42097 Wuppertal, Germany
Corresponding author: a firstname.lastname@example.org
Revised: 5 November 2008
Published online: 7 November 2009
The low energy behaviour of the two-dimensional antiferromagnetic Heisenberg model is studied in the sector with total spins S = 0,1,2 by means of a renormalization group procedure, which generates a recursion formula for the interaction matrix ΔS(n+1) of 4 neighbouring “n clusters” of size 2n × 2n, n = 1,2,3,... from the corresponding quantities ΔS(n). Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies ES(n+1), S = 0,1,2 approach each other for increasing n, i.e. system size. The most relevant couplings in the interaction matrices are generated by the transitions 〈S',m';n+1|Sq*|S,m;n+1〉 between the ground states |S,m;n+1〉 (m = -S,...,S) on an (n+1)-cluster of size 2n+1 × 2n+1, mediated by the staggered spin operator Sq*.
PACS: 71.10.Fd – Lattice fermion models / 71.27.+a – Strongly correlated electron systems; heavy fermions / 75.10.-b – General theory and models of magnetic ordering / 75.10.Jm – Quantized spin models
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2009