Spin Gap in Two-Dimensional Heisenberg Model for CaV$_4$O$_9$

TL;DR

This paper explores the origin of the spin gap in a 2D Heisenberg model relevant to CaV$_4$O$_9$, identifying four-site plaquette singlets as the key mechanism through perturbation and quantum Monte Carlo methods.

Contribution

It reveals that the spin gap in the model arises from four-site plaquette singlets, contrasting with the dimer gap mechanism in similar models.

Findings

Spin gap attributed to four-site plaquette singlets

Perturbation expansion supports plaquette mechanism

Quantum Monte Carlo confirms the plaquette origin

Abstract

We investigate the mechanism of spin gap formation in a two-dimensional model relevant to Mott insulators such as CaV$_4$O$_9$. From the perturbation expansion and quantum Monte Carlo calculations, the origin of the spin gap is ascribed to the four-site plaquette singlet in contrast to the dimer gap established in the generalized dimerized Heisenberg model.