On The Violation Of Marshall-Peierls Sign Rule In The Frustrated $J_{1}-J_{2}$ Heisenberg Antiferromagnet

Abstract

We present a number of arguments in favor of the suggestion that the Marshall-Peierls sign rule survives the frustration in the square-lattice Heisenberg antiferromagnet with frustrating next-nearest-neighbor (diagonal) bonds ($J_{1}-J_{2}$ model) for relatively large values of the parameter $J_{2}/J_{1}$. Both the spin-wave analysis and the exact-diagonalization data concerning the weight of Marshall states support the above suggestion.