Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm

We have developed an improved version of the quantum transfer-matrix algorithm. The extreme eigenvalues and eigenvectors of the transfer matrix are calculated by the recently developed look-ahead Lanczos algorithm for non-Hermitian matrices with higher efficiency and accuracy than by the power method. We have applied this method to the antiferromagnetic Heisenberg ladder. The temperature dependence of the susceptibility, specific heat, correlation length, and nuclear spin relaxation rate 1/${\mathit{T}}_1$ are calculated. Our results support the existence of a spin gap of about 0.5J.