Marvin Leusch | Searcharxiv

arXiv2026

Magnetic instabilities in three- and higher-dimensional Hubbard models with different lattice geometries: Impact of nonlocal spatial correlations

We analyze the impact of the lattice geometry on the thermodynamic transition to magnetically ordered phases in strongly interacting electron systems for various Bravais lattices in three, four and five dimensions, including both local and nonlocal correlation effects. In a first step we use the dynamical mean-field theory (DMFT), which takes into account purely local correlations, to calculate the magnetic susceptibilities of the Hubbard model on three- (3d-sc), four- (4d-sc), and five-dimensional (5d-sc) simple cubic/hypercubic, as well as on three-dimensional body- (bcc) and face-centered (fcc) cubic lattices, and determine the transition temperature to the corresponding magnetically ordered state. In a second step, we exploit the dynamical vertex approximation (D$Γ$A), a diagrammatic extension of DMFT, to include the effect of nonlocal correlations which are particularly important in the vicinity of the corresponding phase transition. For the bipartite 3d-sc, 4d-sc, 5d-sc and bcc lattices nonlocal fluctuations lead to a substantial reduction of the DMFT transition temperature consistent to the overall tendency of mean-field approaches to overestimate the stability of ordered phases. As expected, the magnitude of the difference between the DMFT, being exact in the limit of large connectivity/dimensions, and D$Γ$A transition temperatures decreases with increasing coordination number. On a more practical perspective, these results also provide a reasonable guidance to evaluate the expected overestimation of the DMFT ordering temperature for different material geometries. For the fcc lattice, on the other hand, the ordered phase observed in DMFT vanishes completely within D$Γ$A which is consistent with the existence of strong geometric frustration in this lattice.

cond-mat.str-el↗

arXiv2025

Suppression of the charge fluctuations by nonlocal correlations close to the Mott transition

In this paper, we investigate the impact of nonlocal correlations on charge fluctuations in the two-dimensional single-band Hubbard model close to the Mott metal-to-insulator transition, employing the ladder dynamical vertex approximation. At half filling and for interaction strengths and temperatures where the system is in the Mott insulating phase, charge fluctuations are strongly suppressed. Under these conditions, dynamical mean-field theory (DMFT) calculations predict a strong enhancement of the charge susceptibility at small (electron or hole) doping. However, these DMFT results include only the effects of purely local correlations despite the importance of nonlocal correlations in two-dimensional systems. We have, hence, carried out ladder dynamical vertex approximation (lD$Γ$A) simulations which allow for the inclusion of such nonlocal correlation effects while retaining the local ones of DMFT. Our lD$Γ$A numerical data show that close to half filling the large uniform charge susceptibility of DMFT is strongly suppressed by nonlocal fluctuations but gradually increases with (electron) doping. At a certain doping value, charge fluctuations eventually become larger in lD$Γ$A with respect to DMFT, indicating that the absence of nonlocal correlations underestimates the mobility of the charge carriers in this parameter regime. This metallization effect is also reflected in an enhancement of the lD$Γ$A kinetic and potential energies and a corresponding reduction of the (absolute value of the) lD$Γ$A Matsubara self-energy with respect to DMFT.

cond-mat.str-el↗