Anomalous Quantum Criticality at a Continuous Metal-Insulator Transition

TL;DR

This paper develops an analytic theory for a Mott-like quantum critical point in the Falicov-Kimball model, revealing anomalous density fluctuations and sub-diffusive metallic behavior near the metal-insulator transition.

Contribution

It provides the first fully analytic description of quantum criticality in the FKM on a Bethe lattice using cluster-DMFT, uncovering anomalous dimensions and sub-diffusive dynamics.

Findings

Density fluctuation modes acquire anomalous dimensions.

Sub-diffusive metal with glassy dynamics exists near the QCP.

The critical point is a singular point where the metallic phase shrinks to zero.

Abstract

The Falicov-Kimball model (FKM) is long known to be the simplest model of correlated fermions exhibiting a novel Mott-like quantum critical point (QCP) assocaited with a {\it continuous} MIT in dimensions $D \geq 3$. It is also known to be isomorphic to an {\it annealed} binary-alloy disorder model. Notwithstanding extensive numerical studies for the FKM, analytic insight into the microscopic processes spawning novel Mott-like quantum criticality is scarce. Here, we develop a fully analytic theory for the Mott-like quantum criticality in the FKM on a hierarchical Cayley tree (Bethe lattice) by utilizing a single input from a 2-site cluster-dynamical mean-field theory (CDMFT). We find that density fluctuation modes acquire anomalous dimensions, originating from infra-red power-law singular cluster self-energies. Interestingly, we uncover, at $T=0$, that this {\it sub-diffusive} metal with glassy dynamics separating a weakly ergodic metal from a non-ergodic insulator shrinks to a single point, namely the Mott-like QCP, at least on the Bethe lattice. We detail the consequences of this anomalous quantum criticality for a range of thermal and dynamical responses in a variety of physical systems that can be effectively modelled by the FKM.