Competing phases in the extended U-V-J Hubbard model near the van Hove fillings

The phase diagram of the two-dimensional extended one-band U-V-J Hubbard model is considered within a mean-field approximation and two- and many-patch renormalization group (RG) approaches near the van Hove band fillings. At small t' and J>0 mean-field and many-patch RG approaches give similar results for the leading spin-density-wave (SDW) instability, while the two-patch RG approach, which predicts a wide region of charge-flux (CF) phase becomes unreliable due to nesting effect. At the same time, there is a complex competition between SDW, CF phases, and d-wave superconductivity in two- and many-patch RG approaches. While the spin-flux (SF) phase is not stable at the mean-field level, it is identified as a possible ground state at J<0 in both RG approaches. With increasing t' the results of all three approaches merge: d-wave superconductivity at J>0 and ferromagnetism at J<0 become the leading instabilities. For large enough V the charge-density-wave (CDW) state occurs.