The spin - 1/2 Heisenberg model on Kagome lattice as a quantum critical system

TL;DR

This study uses exact diagonalization to show that the pure spin-1/2 Heisenberg model on the Kagome lattice is a quantum critical point with a gapless ground state, and that ring-exchange interactions induce short-range correlations resembling a triangular lattice antiferromagnet.

Contribution

It reveals the quantum critical nature of the pure Heisenberg model on Kagome lattice and the effects of ring-exchange coupling on spin correlations and potential ordering.

Findings

Pure Heisenberg model is a quantum critical point.

System becomes more short-ranged with ring exchange.

Spin correlations resemble those of a triangular lattice antiferromagnet.

Abstract

Through exact diagonalization study of the spin - 1/2 Heisenberg model on Kagome lattice with ring-exchange coupling $J_{r}$, we find the pure Heisenberg model with $J_{r}=0$ stands as a quantum critical point, as evidenced by avoided level crossing and divergence of the second derivative of the ground state energy with respect to $J_{r}$ at $J_{r}=0$. The pure Heisenberg model should thus be gapless in the thermodynamic limit, contrary to common beliefs. At the same time, the ring exchange coupling is found to drive the system into a state with more short ranged spin correlation and with a local spin correlation pattern equivalent to that of the antiferromagnetic Heisenberg model on triangular lattice(the peak of spin structure factor moves to the momentum $\vec{q}=(\frac{4\pi}{3},0)$). The resemblance of state with the Marston-Zeng spin Pereils solid state(in terms of dimer-dimer correlation) is also much enhanced by the ring exchange coupling, although it is unclear if such correlation would solidify into static order in the thermodynamic limit.