Quantum criticality with dynamical mean-field theory

Abstract

Quantum phase transitions in strongly correlated electron materials are one of the most intriguing phenomena in condensed matter physics. In fact, the rich phase-diagrams of these systems usually allow for the presence of several quantum phase transitions. At the same time, a comprehensive theoretical description of the quantum critical properties of correlated electrons has been not fully developed yet. For one of the most fundamental model in solid state physics, the 3D Hubbard model, quantum critical behaviour appears to violate the conventional Hertz-Millis- Moriya theory. This unexpected finding has been ascribed to the presence of specific features on the Fermi surface (FS), such as Kohn points and/or lines. If this is the case, the correct description of 3D correlated metal should be already accessible by means of Dynamical Mean Field Theory (DMFT) calculations. DMFT, in fact, preserves the information about the FS geometry and correctly captures temporal fluctuations, crucial for the description of quantum criticality. The main aim of this work is to test the hypothesis that DMFT treatment is sufficient to describe the quantum critical behaviour of 3D correlated metals, without resorting to more advanced (and much heavier!) quantum many-body schemes. Our DMFT results for the hole-doped 3D-Hubbard model have allowed to determine the location of the quantum-critical point of the magnetic transition and to highlight promising trends for the associated quantum critical exponents.