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

TL;DR

This paper introduces an efficient DMRG algorithm for Bethe lattices with spin-1/2 or 1, revealing magnetic ground states, persistent magnetization, and exponential decay of correlations, with implications for understanding quantum magnetism.

Contribution

The paper develops a new DMRG algorithm tailored for Bethe lattices with specific spins, providing accurate results and analytical insights into their magnetic properties.

Findings

Magnetic ground states with spin S(g) = 2^g s are confirmed.

Persistent staggered magnetization observed for large generations.

Exponential decay of short-range spin correlations.

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.