Numerical renormalizationgroup study of lowlying eigenstates of the antiferromagnetic S=1 Heisenberg chain
Abstract
We present results of a numerical renormalizationgroup study of the isotropic S=1 Heisenberg chain. The densitymatrix renormalizationgroup techniques used allow us to calculate a variety of properties of the chain with unprecedented accuracy. The groundstate energy per site of the infinite chain is found to be e_{0}~=1.401 484 038 971(4). Openended S=1 chains have effective S=1/2 spins on each end, with exponential decay of the local spin moment away from the ends, with decay length ξ~=6.03(1). The spinspin correlation function also decays exponentially, and although the correlation length cannot be measured as accurately as the openend decay length, it appears that the two lengths are identical. The string correlation function shows longrange order, with g(∞)~=0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q=π, is the Haldane gap, which we find to be ∆~=0.410 50(2). We find many lowlying excited states, including one and twomagnon states, for several different chain lengths. The magnons have spin S=1, so the twomagnon states are singlets (S=0), triplets (S=1), and quintuplets (S=2). For magnons with momenta near π, the magnonmagnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.
 Publication:

Physical Review B
 Pub Date:
 August 1993
 DOI:
 10.1103/PhysRevB.48.3844
 Bibcode:
 1993PhRvB..48.3844W
 Keywords:

 75.10.Jm;
 Quantized spin models