Critical properties of the half-filled Hubbard model in three dimensions

TL;DR

This study uses the dynamical vertex approximation to incorporate spatial correlations in the three-dimensional half-filled Hubbard model, revealing non-local fluctuation effects on critical behavior and Néel temperature.

Contribution

It introduces a method to include all-length-scale spatial correlations beyond DMFT, showing their impact on critical properties and spectral deviations.

Findings

Deviation from mean-field critical exponents matching 3D Heisenberg universality

Reduction of Néel temperature by approximately 30% due to non-local fluctuations

Quantitative differences in spectral properties between DΓA and DMFT

Abstract

By means of the dynamical vertex approximation (D$\Gamma$A) we include spatial correlations on all length scales beyond the dynamical mean field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to non-local fluctuations are: (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)-ferromagnet and (ii) a sizable reduction of the N\'eel temperature ($T_N$) by $\sim 30%$ for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between D$\Gamma$A and DMFT in different regions of the phase-diagram.