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

We numerically caculate the exact ground state energy E₀(N, δ) and the first excited state energy E₁(N, δ) of the one-dimensional spin-½ alternating antiferromagnetic Heisenberg model [formula omitted] for N=8, 10, ⋯, 20 with N being the number of spins. We employ the finite-size scaling method to determine the critical exponents a, b and v of the energy gain by alternation, the energy gap and the correlation length as defined by [formula omitted] and ξ ∼ ^−v (ξ is the correlation length), respectively. The estimated values are a=1.37±0.09, b=0.79±0.06, v=0.75±0.06. We also analytically calculate ξ and v by the use of the phase Hamiltonian method for comparison with our numerical result.