The ground state energies of antiferromagnetic Heisenberg chains

P.M. van den Broek

Hal Tasaki

P.M. van den Broek

The author calculates lower bounds for the ground state energy of the linear antiferromagnetic Heisenberg chain with nearest- and next-nearest-neighbour interactions. From these lower bounds new upper bounds are derived. Several approximations of the ground state energy given in the literature are compared with these upper and lower bounds. It is found that the best approximation is given by extrapolation from finite cyclic chains. This extrapolation, however, is restricted to certain values of the relative strength of the interactions. Here he extrapolates the ground state energy from finite open chains where no such restriction occurs.

Mário J. de Oliveira

A Monte Carlo method is presented to calculate the largest eigenvalue of a non-negative matrix. The method is applied to the spin-1/2 antiferromagnetic Heisenberg chain. The ground-state energy and the singlet-triplet energy gap are calculated for chains up to N=48. The results are in agreement with results obtained by the power method for small values of N.

András Sütö

Kiyomi Okamoto, Hidetoshi Nishimori, Y‐h. Taguchi

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