Magnetism andd-wave superconductivity on the half-filled square lattice with frustration

Abstract

The role of frustration and interaction strength on the half-filled Hubbard model is studied on the square lattice with nearest- and next-nearest-neighbor hoppings $t$ and ${t}^{\ensuremath{'}}$ using the variational cluster approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual N\'eel phase, stable at small frustration ${t}^{\ensuremath{'}}∕t$, and the so-called collinear (or superantiferromagnet) phase with ordering wave vector $(\ensuremath{\pi},0)$ or $(0,\ensuremath{\pi})$, stable for large frustration. These are separated by a phase with no detectable long-range magnetic order. We also find the $d$-wave superconducting (SC) phase $({d}_{{x}^{2}\ensuremath{-}{y}^{2}})$, which is favored by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have nonzero values. In addition, the physics of the metal-insulator transition in the normal state is analyzed. The results obtained with the help of the VCA method are compared with the large-$U$ expansion of the Hubbard model and known results for the frustrated ${J}_{1}\ensuremath{-}{J}_{2}$ Heisenberg model. These results are relevant for pressure studies of undoped parents of the high-temperature superconductors: we predict that an insulator to $d$-wave SC transition may appear under pressure.