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

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 $U_{\mathrm{stiff}}^{\ast }\approx 6$ and the spin-wave energy ${\omega }_M$ at ${\mathbf{q}}_M=(2\pi /3,0)$ etc. is found to vanish at $U_M^{\ast }\approx 6.8$ due to competing spin couplings generated at finite $U$. The loss of magnetic order due to the magnetic instability at ${\mathbf{q}}_M$ yields a first-order quantum phase transition in the insulating state at $U=U_{\mathrm{M}}^{\ast }$. Implications of the quantum spin disordered insulator to the spin-liquid state and Mott transition in the organic systems $\kappa -(\mathrm{BEDT}-\mathrm{TTF}{)}_2\mathrm{X}$ are discussed. Effects of hole and electron doping on magnetic ordering and spin stiffness are also examined.

role of q_M instability, additional references

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