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

Abstract

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 $<S^{\prime },m^{\prime };n+1|S_q^{\ast }|S,m;n+1>$ 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 $S_q^{\ast }$

18 pages, 8 figures, RevTex

References in corpus (4)

• Numerical Contractor Renormalization Method for Quantum Spin Models
• Quantum Phase Transition in a Heisenberg Antiferromagnet on a Square Lattice with Strong Plaquette Interactions
• Neel order in the two-dimensional S=1/2 Heisenberg Model
• Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes

Cited by in corpus (1)

• Deconfinement phase transition in a two-dimensional model of interacting $2\times 2$ plaquettes