Eur. Phys. J. B 72, 541-558 (2009)
https://doi.org/10.1140/epjb/e2009-00381-2

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 fledderj@physik.uni-wuppertal.de

Received: 7 May 2008
Revised: 5 November 2008
Published online: 7 November 2009

Abstract

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 Δ_S⁽ⁿ⁺¹⁾ of 4 neighbouring “n clusters” of size 2ⁿ × 2ⁿ, n = 1,2,3,... from the corresponding quantities Δ_S⁽ⁿ⁾. Conservation of total spin S is implemented explicitly and plays an important role. It is shown, how the ground state energies E_S⁽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|S_q^*|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 S_q^*.