Projected BCS Wave Functions for Low Dimensional Frustrated Spin Systems

TL;DR

This paper introduces a projected BCS wave function as an accurate variational ansatz for the ground state of frustrated spin-half systems, especially the $J_1$-$J_2$ Heisenberg model, capturing quantum spin liquid behavior.

Contribution

It demonstrates that a carefully parameterized fermionic BCS wave function can accurately describe the ground state of strongly frustrated spin systems, advancing the understanding of spin liquids.

Findings

Achieved highly accurate ground state approximation for the $J_1$-$J_2$ model.

Validated the wave function's relevance for non-magnetic quantum phases.

Provided a physically transparent fermionic representation of RVB states.

Abstract

Twenty-five years after the first proposal, the question whether the ground state of a frustrated spin-half system is well described by a spin-liquid Resonating Valence Bond (RVB) wave function is still controversial. A physically transparent representation of a RVB state can be obtained in fermionic representation with a standard BCS-type pairing wave function, working in the subspace with fixed number of electrons and no double occupancies. In this work, we show that, using this variational wave function with a careful parameterization of the pairing function, it is possible to obtain an extremely accurate {\em ansatz} for the ground state of the Heisenberg antiferromagnet with next-nearest neighbors interactions ($J_{1}{-}J_{2}$ model) in the regime of strong frustration. Indeed, in the spin-half realization of this model, it is known that the combined effect of frustration and zero-point motion interferes with the mechanism of spontaneously broken symmetry, giving rise to a non-magnetic phase of purely quantum-mechanical nature ($J_2/J_1\simeq 0.5$). This wave function is proposed to represent the generic spin-half RVB ground state in spin liquids.