Finite-$U$ induced competing interactions, frustration, and quantum phase transition in a triangular-lattice antiferromagnet

TL;DR

This paper investigates how finite on-site Coulomb interaction $U$ induces competing interactions and frustration in a triangular-lattice antiferromagnet, leading to a quantum phase transition from magnetic order to a disordered state.

Contribution

It provides a detailed analysis of the $U$-dependent magnetic instability and identifies the first-order quantum phase transition point in the Hubbard model on a triangular lattice.

Findings

Spin stiffness vanishes at $U^*_{stiff} \\approx 6$

Spin-wave energy at ${\bf q}_M$ vanishes at $U^*_{M} \\approx 6.8$

First-order quantum phase transition occurs at $U=U^*_{M}$

Abstract

The $120^0$ ordered antiferromagnetic state of the Hubbard model on a triangular lattice presents an interesting case of $U$-controlled competing interactions and frustration. The spin stiffness is found to vanish at $U^* _{\rm stiff} \approx 6$ and the spin-wave energy $\omega_M$ at ${\bf q}_M=(2\pi/3,0)$ etc. is found to vanish at $U_M ^* \approx 6.8$ due to competing spin couplings generated at finite $U$. The loss of magnetic order due to the magnetic instability at ${\bf q}_M$ yields a first-order quantum phase transition in the insulating state at $U=U_{\rm M}^*$. Implications of the quantum spin disordered insulator to the spin-liquid state and Mott transition in the organic systems $\rm \kappa -(BEDT-TTF)_2 X$ are discussed. Effects of hole and electron doping on magnetic ordering and spin stiffness are also examined.