Frustration in the Hubbard model: a quantum cluster study

The role of frustration in the Hubbard model is studied on the square lattice with nearest and next-nearest neighbour hoppings $t$ and $t'$ using the Variational cluster perturbation theory (VCPT, see [1]). We find two phases with long-range magnetic order: the usual antiferromagnet (AF1) phase, stable at small $t'/t,$ and the so-called superantiferromagnetic phase (AF2) for large frustration. These are separated by a phase with no magnetic order. We also find d-wave superconductivity (d$_{x2-y2})$ for small values of $U\le $4$t$ and sufficiently weak frustration. The Mott-Hubbard transition is discussed in this context. We also compare the classical phase diagram obtained from the large-U expansion with that of the frustrated J$_{1}$-J$_{2}$ Heisenberg model. \newline \newline [1] M. Potthoff, M. Aichhorn, C. Dahnken, Phys. Rev. Lett. \textbf{91}, 206402 (2003).