Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach

TL;DR

This study uses advanced variational Monte Carlo methods to explore the phase competition in a frustrated spin-1/2 Heisenberg model on the kagome lattice, revealing that small ferromagnetic next-nearest interactions stabilize a valence-bond crystal over the Dirac spin liquid.

Contribution

It introduces an extended variational wave function approach to identify the stabilization of a valence-bond crystal in the kagome Heisenberg model with next-nearest interactions.

Findings

Small ferromagnetic J2 stabilizes a 36-site VBC.

Dirac spin liquid remains a local minimum.

VBC has a non-trivial flux pattern and large dimerization.

Abstract

The highly-frustrated spin-1/2 quantum Heisenberg model with both nearest ($J_1$) and next-nearest ($J_2$) neighbor exchange interactions is revisited by using an extended variational space of projected wave functions that are optimized with state-of-the-art methods. Competition between modulated valence-bond crystals (VBCs) proposed in the literature and the Dirac spin liquid (DSL) is investigated. We find that the addition of a {\it small} ferromagnetic next-nearest-neighbor exchange coupling $|J_2|>0.09 J_1$ leads to stabilization of a 36-site unit cell VBC, although the DSL remains a local minimum of the variational parameter landscape. This implies that the VBC is not trivially connected to the DSL: instead it possesses a non-trivial flux pattern and large dimerization.