Variational Monte Carlo study of gapless spin liquid in the spin-$1/2$ XXZ antiferromagnetic model on the kagome lattice

TL;DR

This study uses variational Monte Carlo methods to investigate the ground state of the spin-1/2 XXZ antiferromagnetic model on the kagome lattice, revealing a stable gapless U(1) Dirac spin liquid with no magnetic order or spin gap.

Contribution

It demonstrates that the U(1) Dirac spin liquid is the optimal variational state across the XY to Heisenberg regimes, with no energy advantage in gauge symmetry breaking.

Findings

Magnetic states are unstable in the thermodynamic limit.

No energy gain from gauge symmetry breaking from U(1) to Z2.

A gapless S=2 spin excitation is observed.

Abstract

By using the variational Monte Carlo technique, we study the spin-$1/2$ XXZ antiferromagnetic model (with easy-plane anisotropy) on the kagome lattice. A class of Gutzwiller projected fermionic states with a spin Jastrow factor is considered to describe either spin liquids (with $U(1)$ or $Z_2$ symmetry) or magnetically ordered phases (with ${\bf q}=(0,0)$ or ${\bf q}=(4\pi/3,0)$). We find that the magnetic states are not stable in the thermodynamic limit. Moreover, there is no energy gain to break the gauge symmetry from $U(1)$ to $Z_2$ within the spin-liquid states, as previously found in the Heisenberg model. The best variational wave function is therefore the $U(1)$ Dirac state, supplemented by the spin Jastrow factor. Furthermore, a vanishing $S=2$ spin gap is obtained at the variational level, in the whole regime from the $XY$ to the Heisenberg model.