Emergent soft-gap Anderson models at quantum criticality in a lattice Hamiltonian within dynamical mean field theory

TL;DR

This study reveals the emergence of a soft-gap spectrum at a quantum critical point in a lattice model within dynamical mean field theory, linking local quantum criticality to lattice models and non-Fermi liquid behavior.

Contribution

It demonstrates the emergence of a soft-gap $|omega|^r$ spectrum at a lattice quantum critical point, connecting impurity models to lattice models in dynamical mean field theory.

Findings

Emergence of a soft-gap spectrum at the QCP.

Temperature-independent, isosbestic exponent at the QCP.

Connection between local quantum criticality and lattice models.

Abstract

Local quantum criticality in itinerant fermion systems has been extensively investigated through the soft-gap Anderson impurity model, wherein a localized, correlated impurity, hybridizes with a broad conduction band with a singular, $|\omega|^r$, density of states. However, lattice models hosting quantum critical points (QCPs), do not appear to have such a spectrum emerging at the QCP. In this work, we report the emergence of such a singular form of the density of states in a three-orbital lattice model, within dynamical mean field theory, precisely at a quantum critical point, separating a gapless, Fermi liquid, metallic phase from a gapped, Mott insulating phase. A temperature-dependent exponent, $\alpha$, defined using the corresponding Matsubara self-energy, is found to vary from $+1$ deep in the FL regime, to $-1$ in the Mott insulator regime. Interestingly, we find that $\alpha$ becomes temperature independent, and hence isosbestic, precisely at the QCP. The isosbestic exponent is shown to lead to an emergent soft-gap spectrum, $|\omega|^r$ at the QCP, where $r = |\alpha_{\rm iso}|$. We discuss the implications of our findings for non-Fermi liquid behaviour in the quantum critical region of the phase diagram.