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

Abstract

We present analytical and numerical calculations for some excited states of the frustrated J 1− J 2 spin- 1 2 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 S total z . 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 J 2.