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Journal of the Physical Society of Japan

A Numerical Study of Spin-1/2 Alternating Antiferromagnetic Heisenberg Linear Chains

Kiyomi Okamoto, Hidetoshi Nishimori, Y‐h. Taguchi

Published May 15, 1986• 35 citations
Publisher

Abstract

We numerically caculate the exact ground state energy E 0 ( N , δ) and the first excited state energy E 1 ( N , δ) of the one-dimensional spin-(\frac{1}{2}) alternating antiferromagnetic Heisenberg model
DOI
10.1143/jpsj.55.1458

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Alternation rarameter δ dependences of the ground-state energy (GE) ε (δ) and the gap Δ (δ) in the excitation spectrum of the spin Hamiltonian H = J ∑ l =1 N [1+(-1) l δ] [ S l x S l +1 x + S l y S l +1 y +σ S l z S l +1 z ] are calculated in two numerical methods, with interest in the exponents β of the GE and α of the gap which are defined as ε (δ) - ε (0)∝δ β and Δ (δ)∝δ α for small δ. First by means of the 2-level renormalization group calculation the exponents are obtained as β∼1.78 and α∼0.96 for the isotropic Heisenberg model (σ=1). Second by means of the finite chain extrapolation, β for σ=1 is obtained as 1.68 -0.36 +0.13 from the data of the extrapolated GE between δ=0.05 and 0.1.
One dimensional S =1 antiferromagnetic Heisenberg chains with bond alternation and uniaxial single-ion-type anisotropy are studied by numerical exact diagonalization of finite size systems. We calculate the ground state phase diagram using the twisted boundary condition method for D ≥0. The ground states of this model contain the Haldane state, large- D state and the dimer state. Using conformal field theory and the level spectroscopy method, we calculate the D and δ-dependence of the Luttinger liquid paraments K and the critical exponent ν of the energy gap.