Marshall-Peierls Sign Rule in Frustrated Heisenberg Chains

We consider the frustrated antiferromagnetic s=1 Heisenberg quantum spin chain with regard to the Marshall-Peierls sign rule. Using exact diagonalization data we investigate the breakdown of the Marshall- Peierls sign rule in dependence on frustration and compare our findings with data for s=1/2. We calculate a critical value of frustration J$\text{}_{2}^{crit}$, where the Marshall-Peierls sign rule is violated. The extrapolation of this value to the infinite chain limit holds J$\text{}_{2}^{crit}$ ≈ 0.016, lower than in the case of s=1/2 (J$\text{}_{2}^{crit}$ ≈ 0.027). T his points to a stronger influence of frustration in the case of s=1. Nevertheless, the calculation of the weight of the Ising-states violating the Marshall- Peierls sign rule shows that the latter holds approximately even for a quite large frustration and may be used for numerical techniques.