Resonating-Valence-Bond Ground-state of CaV$_4$O$_9$ by the Gutzwiller-projected Schwinger-boson method

TL;DR

This paper investigates the ground state of CaV$_4$O$_9$ using a Gutzwiller-projected Schwinger-boson method within a variational Monte Carlo framework, revealing a resonating-valence-bond state with specific magnetic and spectral properties.

Contribution

It introduces a novel variational wave function approach for the Heisenberg model on a depleted lattice, achieving the lowest energy state reported and analyzing its magnetic and excitation characteristics.

Findings

The optimized state has an energy of -0.5510J.

Néel order persists with no gap at isotropic coupling.

The study provides detailed calculations of bond energies, magnetization, and excitation spectrum.

Abstract

An antiferromagnetic Heisenberg model on a 1/5-depleted two-dimensional square-lattice, a model of CaV$_4$O$_9$, is investigated by variational Monte Carlo simulation. A prototype of a trial wave function is made by projecting out the doubly occupied states from the Schwinger-boson mean-field solution. Then variational Monte Carlo simulation is performed up to $40 \times 40 $ sites(including $320$ vacant sites). The optimized state has the lowest energy, $-0.5510J$, ever reported. For this state energies of a dimer bond and a plaquette bond, staggered magnetization, static structure factor, and excitation spectrum are calculated. It is shown that the N\'eel order survives and there is no gap at isotropic coupling.