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 twoand many-patch renormalization-group ~RG! approaches near the Van Hove band fillings. At small t8 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 that predicts a wide region of charge-flux ~CF! phase becomes unreliable due to nesting effect. There is a complex competition between SDW, CF phases, and d-wave superconductivity at small t8 in twoand many-patch RG approaches. The spin-flux phase, which is not stable at the mean-field level, is identified as a possible ground state at J,0 in both RG approaches. With increasing t8 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-densitywave state occurs.