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Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration $t'/t$ could change the wave vector of maximum spin correlation along ($π,π$)$\rightarrow$($π,\frac{5π}{6}$)$\rightarrow$($\frac{5π}{6},\frac{5π}{6}$)$\rightarrow$ ($\frac{2π}{3},\frac{2π}{3}$), indicating the frustration's remarkable effect on the magnetism. In the studied filling region <n>=1.0-1.3, the doping behaves like some kinds of {\it{frustration}}, which destroys the $(π,π)$ AFM correlation quickly and push the magnetic order to a wide range of the $(\frac{2π}{3},\frac{2π}{3})$ $120^{\circ}$ order when the $t'/t$ is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.