Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

Details Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model Real space renormalization group approach to the 2d antiferromagnetic Heisenberg model

2008-11-04

arxiv.org/abs/0811.0526v2

Eur. Phys. J. B 72, 541-558 (2009)

Physics

Condensed Matter

Strongly Correlated Electrons

18 pages, 8 figures, RevTex

Scientific paper

10.1140/epjb/e2009-00381-2

The low energy behaviour of the 2d 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 $\Delta_S^{(n+1)}$ of 4 neighbouring "$n$ clusters" of size $2^n\times 2^n$, $n=1,2,3,...$ from the corresponding quantities $\Delta_S^{(n)}$. 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 $$ between the ground states $|S,m;n+1>$ ($m=-S,...,S$) on an $(n+1)$-cluster of size $2^{n+1}\times 2^{n+1}$, mediated by the staggered spin operator $S_q^*$

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