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

TL;DR

This study investigates how frustration and interaction strength influence magnetic and superconducting phases in the half-filled Hubbard model on a square lattice, revealing phase coexistence and potential pressure-induced transitions.

Contribution

It introduces a detailed phase diagram of magnetic and superconducting states using VCA, highlighting coexistence regions and pressure-related transitions in the Hubbard model.

Findings

Identification of Neel and collinear magnetic phases separated by a non-magnetic phase.

Discovery of a broad region where antiferromagnetism and d-wave superconductivity coexist.

Prediction of an insulator to d-wave superconductor transition under pressure.

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 neighbour hoppings t and t' using the Variational Cluster Approximation (VCA). At half-filling, we find two phases with long-range antiferromagnetic (AF) order: the usual Neel phase, stable at small frustration t'/t, and the so-called collinear (or super-antiferromagnet) phase with ordering wave-vector $(\pi,0)$ or $(0,\pi)$, 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 ($d_{x^2-y^2}$), which is favoured by frustration if it is not too large. Intriguingly, there is a broad region of coexistence where both AF and SC order parameters have non-zero 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 J1-J2 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.