Valence-bond crystal in the extended kagome spin-12quantum Heisenberg antiferromagnet: A variational Monte Carlo approach

Abstract

The highly frustrated spin-$\frac{1}{2}$ 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 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 nontrivial flux pattern and large dimerization.