Improved variational wave function for the two-dimensional spin-1/2 Heisenberg antiferromagnet

Abstract

We present a variational wave function for the ground state of the two-dimensional spin-1/2 Heisenberg antiferromagnet. It is a modification of a Monte Carlo variational wave function proposed by Huse and Elser which gives excellent results for the ground-state energy but breaks the rotational symmetry of the squared staggered magnetization. In their case the x component of the squared staggered magnetization (${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$ is much larger than (${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$ and (${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$${)}^{2}$, which are the y and z components, respectively. In this paper we show how to restore the symmetry between ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ and ${\mathit{m}}_{\mathit{y}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. However, ${\mathit{m}}_{\mathit{z}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$ is still much smaller than ${\mathit{m}}_{\mathit{x}}^{\mathrm{\ifmmode^\circ\else\textdegree\fi{}}}$. We also study the enforcement of the full rotational symmetry in our trial wave function using only two spin interaction terms. Finally, we discuss how errors in Monte Carlo data affect the efficiency of algorithms which determine more systematically the best variational parameters for the ground-state wave function.