Comment on ``Magnetic Susceptibility of the two-dimensional Hubbard model ''

TL;DR

This paper demonstrates through Monte Carlo simulations that the magnetic susceptibility behavior in the two-dimensional Hubbard model at intermediate coupling and low temperature aligns with experimental observations in high-temperature superconductors, challenging previous assumptions about the necessary coupling strength.

Contribution

The study shows that the magnetic susceptibility behavior can be reproduced at intermediate coupling regimes, not just large coupling, when low enough temperatures are considered, highlighting the limitations of GRPA.

Findings

Susceptibility increases with doping at intermediate coupling.

Behavior consistent with experimental high-Tc superconductor data.

GRPA fails to predict magnetic transition in this regime.

Abstract

The observed magnetic spin susceptibility of high-temperature superconductors such as La$_{2- x}$Sr$_x$CuO$_4$ increases when $x$ increases from zero, i.e. as one dopes away from half-filling. Recent Monte Carlo simulations of A. Moreo (Phys. Rev. B {\bf 48}, 3380 (1993)) suggest that this behavior can be reproduced by the two-dimensional Hubbard model only at large coupling, namely, $U/t$ of order $10$. Using longer runs, our Monte Carlo simulations show that the same behavior as for $U/t=10$ is obtained even in the intermediate coupling regime ($U/t=4$), as long as the temperature is low enough ($T=t/6$) that strong antiferromagnetic correlations are building up at half-filling. These results are consistent with the fact that in two-dimensions, the GRPA should fail in the parameter range where it predicts a magnetic phase transition.