NUMERICAL RENORMALIZATION-GROUP STUDY OF LOW-LYING EIGENSTATES OF THE ANTIFERROMAGNETIC S = 1 HEISENBERG CHAIN

We present results of a numerical renormalization-group study of the isotropic S = 1 Heisenberg chain. The density-matrix renormalization-group techniques used allow us to calculate a variety of properties of the chain with unprecedented accuracy. The ground state energy per site of the infinite chain is found to be e0 congruent-to -1.401 484 038 971(4). Open-ended 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 xi congruent-to 6.03(1). The spin-spin correlation function also decays exponentially, and although the correlation length cannot be measured as accurately as the open-end decay length, it appears that the two lengths are identical. The string correlation function shows long-range order, with g(infinity) congruent-to -0.374 325 096(2). The excitation energy of the first excited state, a state with one magnon with momentum q = pi, is the Haldane gap, which we find to be DELTA congruent-to 0.410 50(2). We find many low-lying excited states, including one- and two-magnon states, for several different chain lengths. The magnons have spin S = 1, so the two-magnon states are singlets (S = 0), triplets (S = 1), and quintuplets (S = 2). For magnons with momenta near pi, the magnon-magnon interaction in the triplet channel is shown to be attractive, while in the singlet and quintuplet channels it is repulsive.