Finite size scaling for low energy excitations in integer Heisenberg spin chains

摘要

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 behaviour (with L as the chain length) for medium chain length to 1/L(sup 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. (author). 23 refs, 5 figs. (Atomindex citation 28:022279)