Spin-$\frac{1}{2}$ Heisenberg $J_1$-$J_2$ antiferromagnet on the kagome lattice

TL;DR

This study uses variational Monte Carlo with Gutzwiller projected fermionic states to explore the phase diagram of the spin-1/2 Heisenberg model on the kagome lattice, revealing stability of the U(1) Dirac spin liquid and the emergence of magnetic order at higher J2.

Contribution

It demonstrates that a gapped Z2 spin liquid can be stabilized on finite clusters with J2, but the U(1) Dirac spin liquid remains stable in the thermodynamic limit, and identifies the transition to magnetic order.

Findings

Gapped Z2 spin liquid stabilized on finite clusters with J2.

U(1) Dirac spin liquid remains stable in the thermodynamic limit.

Magnetic order emerges for J2/J1 > 0.3.

Abstract

We report variational Monte Carlo calculations for the spin-$\frac{1}{2}$ Heisenberg model on the kagome lattice in the presence of both nearest-neighbor $J_1$ and next-nearest-neighbor $J_2$ antiferromagnetic superexchange couplings. Our approach is based upon Gutzwiller projected fermionic states that represent a flexible tool to describe quantum spin liquids with different properties (e.g., gapless and gapped). We show that, on finite clusters, a gapped $\mathbb{Z}_{2}$ spin liquid can be stabilized in the presence of a finite $J_2$ superexchange, with a substantial energy gain with respect to the gapless $U(1)$ Dirac spin liquid. However, this energy gain vanishes in the thermodynamic limit, implying that, at least within this approach, the $U(1)$ Dirac spin liquid remains stable in a relatively large region of the phase diagram. For $J_2/J_1 \gtrsim 0.3$, we find that a magnetically ordered state with ${\bf q}={\bf 0}$ overcomes the magnetically disordered wave functions, suggesting the end of the putative gapless spin-liquid phase.