Magnetic properties and superconductivity in the two-dimensional repulsive Hubbard model

TL;DR

This study introduces a new method within the strong coupling diagram technique to accurately estimate parameters that satisfy the Mermin-Wagner theorem in the 2D Hubbard model, revealing conditions for superconductivity.

Contribution

It proposes a novel parameter estimation method in SCDT for the 2D Hubbard model and investigates superconductivity, identifying a $d_{x^2-y^2}$ pairing transition in a modified model.

Findings

Good agreement of magnetic quantities with experiments

Superconducting transition found in the $t$-$t'$-$t''$-$U$ model at $T_c\approx0.016t$

No superconductivity in the $t$-$U$ model

Abstract

A new method for estimating the parameter ensuring the fulfillment of the Mermin-Wagner theorem in the strong coupling diagram technique (SCDT) for the two-dimensional Hubbard model is suggested. With the precise parameter value, calculated magnetic quantities are in good agreement with the results of numeric and optical-lattice experiments. Obtained spin and charge vertices are used for investigating superconductivity in the $t$-$U$ and $t$-$t'$-$t"$-$U$ Hubbard models in the regime of strong correlations. We found no superconducting transition in the $t$-$U$ model. In the $t$-$t'$-$t"$-$U$ model, the transition occurs for the singlet $d_{x^2-y^2}$ pairing at $T_c\approx0.016t$. The difference between the two models is in the renormalized hopping describing electron motion in SCDT. In the $t$-$U$ model, it vanishes for momenta $(\pi,0)$, $(0,\pi)$ of extrema of the $d$-wave order parameter, while the hopping is finite in the $t$-$t'$-$t"$-$U$ model. In the one-band model, there are optimal values of $t'$ and $t"$ ensuring the highest $T_c$.