Frequency-dependent spin susceptibility in the two-dimensional Hubbard model

TL;DR

This study uses Quantum Monte Carlo methods to calculate the dynamical spin susceptibility in the half-filled 2D Hubbard model at finite temperature, revealing deviations from RPA predictions and supporting a self-consistent renormalization approach.

Contribution

It introduces an analytical continuation technique for Green's functions and provides new insights into spin dynamics beyond RPA in the 2D Hubbard model.

Findings

Contradicts RPA prediction of long-range antiferromagnetic order at T=0.2t

Supports self-consistent renormalization approach of Moriya

Static susceptibility aligns with low-frequency simulation results

Abstract

A Quantum Monte Carlo calculation of dynamical spin susceptibility in the half-filled 2D Hubbard model is presented for temperature $T=0.2t$ and an intermediate on-site repulsion $U=4t$. Using the singular value decomposition technique we succeed in analytically continuing the Matsubara Green's function into the real frequency domain and in deriving the spectral representation for the longitudinal and transverse spin susceptibility. The simulation results, while contradicting the random-phase approximation prediction of antiferromagnetic long-range order at this temperature, are in agreement with an extension of a self-consistent renormalization approach of Moriya. The static susceptibility calculated using this technique is qualitatively consistent with the $\omega \rightarrow 0 $ simulation results.