Density matrix renormalization group algorithm for Bethe lattices of spin 1/2 or 1 sites with Heisenberg antiferromagnetic exchange

Abstract

An efficient density matrix renormalization group (DMRG) algorithm is presented for the Bethe lattice with connectivity $Z=3$ and antiferromagnetic exchange between nearest neighbor spins $s=1/2$ or 1 sites in successive generations $g$. The algorithm is accurate for $s=1$ sites. The ground states are magnetic with spin $S(g)=2^{g}s$, staggered magnetization that persists for large $g>20$ and short-range spin correlation functions that decrease exponentially. A finite energy gap to $S>S(g)$ leads to a magnetization plateau in the extended lattice. Closely similar DMRG results for $s$ = 1/2 and 1 are interpreted in terms of an analytical three-site model.

7 Pages and 8 figures