Competing phases in the extended U-V-J Hubbard model near the Van Hove fillings -: art. no. 125104

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 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 t(') in two- and 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 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 state occurs.