Finite Size Scaling for Low Energy Excitations in Integer Heisenberg Spin Chains

Abstract

In this paper we study the finite size scaling for low energy excitations of $S=1$ and $S=2$ Heisenberg chains, using the density matrix renormalization group technique. A crossover from $1/L$ behavior (with $L$ as the chain length) for medium chain length to $1/L^2$ scaling for long chain length is found for excitations in the continuum band as the length of the open chain increases. Topological spin $S=1/2$ excitations are shown to give rise to the two lowest energy states for both open and periodic $S=1$ chains. In periodic chains these two excitations are ``confined'' next to each other, while for open chains they are two free edge 1/2 spins. The finite size scaling of the two lowest energy excitations of open $S=2$ chains is determined by coupling the two free edge $S=1$ spins. The gap and correlation length for $S=2$ open Heisenberg chains are shown to be 0.082 (in units of the exchange $J$) and 47, respectively.

4 pages (two column), PS file, to be appear as a PRB Brief Report

References in corpus (4)

• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Finite-lattice extrapolations for a Haldane gap antiferromagnet
• Impurity state in Haldane gap for S=1 Heisenberg antiferromagnetic chain with bond doping
• Impurity Energy Level Within The Haldane Gap

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