A DENSITY-MATRIX RENORMALIZATION-GROUP APPROACH TO INTERACTING QUANTUM-SYSTEMS ON CAYLEY TREES

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