Magnetic and pair correlations of the Hubbard model with next-nearest-neighbor hopping

TL;DR

This study combines analytical methods and quantum Monte Carlo simulations to explore magnetic and pairing correlations in a Hubbard model with next-nearest-neighbor hopping, shedding light on high-temperature superconductor behaviors.

Contribution

It introduces a detailed analysis of magnetic and pairing correlations in the Hubbard model with next-nearest-neighbor hopping, highlighting different physical mechanisms at play.

Findings

Magnetic susceptibility peaks at finite doping due to different reasons for t'=-0.35t and t'=0.

Antiferromagnetic fluctuations slightly enhance d-wave superconducting correlations.

Van Hove singularity tends to decrease superconducting correlations in the repulsive model.

Abstract

A combination of analytical approaches and quantum Monte Carlo simulations is used to study both magnetic and pairing correlations for a version of the Hubbard model that includes second-neighbor hopping $t^{\prime }=-0.35t$ as a model for high-temperature superconductors. Magnetic properties are analyzed using the Two-Particle Self-Consistent approach. The maximum in magnetic susceptibility as a function of doping appears both at finite $% t^{\prime }$ and at $t^{\prime }=0$ but for two totally different physical reasons. When $t^{\prime }=0$, it is induced by antiferromagnetic correlations while at $t^{\prime }=-0.35t$ it is a band structure effect amplified by interactions. Finally, pairing fluctuations are compared with $% T $-matrix results to disentangle the effects of van Hove singularity and of nesting on superconducting correlations. The addition of antiferromagnetic fluctuations increases slightly the $d$-wave superconducting correlations despite the presence of a van Hove singularity which tends to decrease them in the repulsive model. Some aspects of the phase diagram and some subtleties of finite-size scaling in Monte Carlo simulations, such as inverted finite-size dependence, are also discussed.