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

TL;DR

This paper investigates whether the Marshall-Peierls sign rule remains valid in the frustrated square-lattice $J_1$-$J_2$ Heisenberg antiferromagnet, using analytical and numerical methods to analyze its robustness.

Contribution

It provides evidence that the Marshall-Peierls sign rule persists in the $J_1$-$J_2$ model despite frustration, supported by spin-wave analysis and exact diagonalization data.

Findings

Marshall-Peierls sign rule survives for large $J_2/J_1$

Spin-wave analysis supports the rule's validity

Exact diagonalization confirms the rule's applicability

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.