Scaling behavior in the S=1 antiferromagnetic XXZ chain (abstract)
Date of Original Version
A recent remarkable prediction by Haldane is the 1D integer spin antiferromagnets of XXZ type should show strikingly different T=0 phase behavior from their counterparts with half‐integer spin. The consensus of a wide variety of numerical evidence is in support of the Haldane prediction. However, one aspect which has been particularly difficult to confirm has been the behavior in the vicinity of the critical point Δ=Δ2. The point Δ2 is predicted to be a second‐order transition in the universality class of the transverse Ising model at its critical field. It has been numerically established that at Δ=Δ2∼1.18–1.20, the Haldane gap disappears and an excited SzT=0 state becomes degenerate with the SzT=0 ground state for Δ≥Δ2. The mapping to the transverse Ising model implies the existence in the limit N→∞ of an infinite continuum of scaling states quasi‐degenerate with the ground state(s) at Δ=Δ2. Numerical calculations to determine the presence of these scaling states have been performed up to N=12 spins for the spin‐1 XXZ model. The development of this scaling continuum is only apparent for large N, when a class of k=0, SzT=0 high‐lying spectral excitations develop a minimum in the vicinity of Δ∼1.18 which intensifies with increasing N. These excitations extrapolate well below the lower edge of the triplet continuum, and we conclude these are the Haldane scaling states. This conclusion is reinforced by a detailed study of the corresponding excitations for the spin‐1/2 transverse Ising model. However, we also find a class of k=0, ‖SzT‖=1 excitations which show similar scaling behavior in the vicinity of Δ2. These states were not included in the Haldane prediction. The implications for the behavior of the correlation functions at Δ2 are discussed. © 1988, American Institute of Physics. All rights reserved.
Journal of Applied Physics
Bonner, J. C., G. Müller, and J. B. Parkinson. "Scaling behavior in the S=1 antiferromagnetic XXZ chain (abstract)." Journal of Applied Physics 63, 8 (1988): 3560. doi:10.1063/1.340716.