Zero temperature dynamics of the Hubbard model in infinite dimensions: A local moment approach

TL;DR

This paper extends the local moment approach within DMFT to analyze the zero-temperature phase diagram of the Hubbard model in infinite dimensions, revealing universal spectral features and Mott transition behavior.

Contribution

It provides a comprehensive zero-temperature phase diagram of the Hubbard model using LMA+DMFT, including spectral, optical, and transition properties, and compares with IPT results.

Findings

LMA improves spectral sum-rule with increasing interaction strength

Universal low-energy spectral scaling extends to infinite frequency at strong coupling

Filling-controlled Mott transition and pseudogap formation near half-filling

Abstract

The local moment approach (LMA) has presented itself as a powerful semi-analytical quantum impurity solver (QIS) in the context of the dynamical mean-field theory (DMFT) for the periodic Anderson model and it correctly captures the low energy Kondo scale for the single impurity model, having excellent agreement with the Bethe ansatz and numerical renormalization group results. However, the most common correlated lattice model, the Hubbard model, has not been explored well within the LMA+DMFT framework beyond the insulating phase. Here in our work, within the framework we attempt to complete the phase diagram of the single band Hubbard model at zero temperature. Our formalism is generic to any particle filling and can be extended to finite temperature. We contrast our results with another QIS, namely the iterated perturbation theory (IPT) and show that the second spectral moment sum-rule improves better as the Hubbard interaction strength grows stronger in LMA, whereas it severely breaks down after the Mott transition in IPT. We also show that, in the metallic phase, the low-energy scaling of the spectral density leads to universality which extends to infinite frequency range at infinite correlation strength (strong-coupling). At large interaction strength, the off half-filling spectral density forms a pseudogap near the Fermi level and filling-controlled Mott transition occurs as one approaches the half-filling. Finally we study optical properties and find universal features such as absorption peak position governed by the low-energy scale and a doping independent crossing point, often dubbed as the "isosbestic point" in experiments.