Marshall-Peierls sign rule for excited states of the frustrated J1−J2 Heisenberg antiferromagnet

We present analytical and numerical calculations for some excited states of the frustrated J1−J2 Heisenberg model for linear chains and square lattices. We consider the lowest eigenstates in the subspaces determined by the eigenvalue M of the spin operator Stotalz. Because of the reduced number of Ising basic states in the subspaces with higher M we are able to diagonalize systems with up to N = 144 spins. We find evidence that the Marshall-Peierls sign rule survives for a relatively large frustration parameter J2.