The Heisenberg model on the Cayley tree

M. Fannes, Bruno Nachtergaele, Reinhard F. Werner

Farrukh Maksutovich Mukhamedov, Abdessatar Souissi

T. Ogawa

The ferromagnetic Heisenberg model on the finite most symmetrical Cayley tree is studied in the limit of large size. The spectrum and wavefunctions of the single-magnon states are obtained rigorously. They have many unusual properties. The magnon density excited as a whole at infinitesimal temperatures is logarithmically divergent when the magnon is approximated as boson. Nevertheless, the possibility of some spontaneous magnetization at the central part of the tree remains.

Antônio Sérgio Teixeira Pires

Minoru Takahashi

Barry Friedman

I have examined the nearest-neighbour quantum Heisenberg model on a Cayley tree using a simple density matrix renormalization group scheme. For spin 1/2 on a three-legged Bethe lattice I find indications of long-range antiferromagnetic order in agreement with the spin wave result. Preliminary calculations using a more complicated density matrix renormalization group scheme give promise that one can treat interacting quantum systems on Cayley trees very accurately.