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Physics Letters A

Real space renormalization group study of the anisotropic quantum Heisenberg model on a square lattice

A. Drzewiński, J. Szṅajd

Published Jun 1, 1989• 9 citations
Publisher
DOI
10.1016/0375-9601(89)90880-3

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Within a real-space renormalization-group framework, the spin-\textonehalf{} Heisenberg ferromagnet in the presence of an Ising-like anisotropy on a self-dual hierarchical lattice is discussed. The results are exact for this lattice but can also be considered as a quite satisfactory approximation for the simple square one. The controversial point on how Tc{T}_{c}Tc​ vanishes in the isotropic Heisenberg limit is analyzed: Quite strong evidence is presented favoring a continuous function of anisotropy. The crossover from the isotropic Heisenberg model to the pure Ising one is exhibited.
We present a quantum cluster solver for the spin- S Heisenberg model on a two-dimensional lattice. The formalism is based on the real-space renormalization procedure and uses the lattice point group-theoretical analysis and non-Abelian SU (2) spin symmetry technique. The exact diagonalization procedure is used twice at each renormalization group step. The method is applied to the spin-half antiferromagnet on a square lattice, and a calculation of local observables is demonstrated. A symmetry-based truncation procedure is suggested and verified numerically.