Finite-Size Corrections and Spin Correlations of Magnetized S=1 Antiferromagnetic Heisenberg Chain

Abstract

The S=1 antiferromagnetic Heisenberg chain in a magnetic field along the z-axis at T=0 is studied by numerical diagonalizations up to N=16 and an analysis of size corrections. We check that the system obeys the conformal field theory with the central charge c=1 in a magnetic state (0<m<1). We investigate the asymptotic form of the transverse and parallel spin correlations and give the exponents η and η^z, defined by ⟨S₀^xS_r^x⟩\simeq(−1)^rr^−η and ⟨S₀^zS_r^z⟩−m²\simeqcos (2k_Fr)r^−ηz. We determine η=1⁄2 and η^z=2 at m=0 and 1. In addition, we check the relation ηη^z=1, which is consistent with the Luttinger liquid concept. In terms of the concept, the anomalies of magnetization at m=0 and 1 are discussed.