Anomalous Quantum Criticality at a Continuous Metal-Insulator Transition

TL;DR

This work develops an analytic framework for the continuous metal-insulator transition in the Falicov-Kimball model by leveraging a single input from a two-site CDMFT analysis on a Bethe lattice. The resulting theory reveals infrared power-law self-energies that yield an infrared-divergent three-leg vertex, driving anomalous, subdiffusive charge dynamics and a Mott-like quantum critical point at T = 0 where ergodicity breaks down. The MIT features non-ergodic LDOS correlations, a diverging quantum geometric tensor, and a coherent picture of heavy d-fermion dynamics that underpin glassy, percolative transport near criticality. Predictions include distinctive optical, thermodynamic, and noise signatures that connect to experiments in correlated oxides and Kondo-like systems, providing a unifying view of subdiffusion, non-ergodicity, and quantum geometry at a Mott transition driven by annealed disorder.

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.

Figures (3)

• Figure 1: (Color online) Exponent of $\rho_{00}(\omega)$ and $Im\Sigma_{00}(\omega)$ closed to the Fermi energy at critical value of U with symmetric alloy
• Figure 2: (Color online) Optical Conductivity of the completely random ($f_{0\alpha}=0$) FKM within two-site CDMFT, showing its evolution with $U$ at temperature $T\rightarrow 0$. The MIT occurs at $U_{c}=1.8$. Blue symbols show how an emergent scale, $\Omega_{0}(U)$, associated with a smooth crossover between metallic and insulating states, collapses at the Mott transition ($U=1.8$) as $(\delta U)^{\nu}$ with $\nu=1.29$, close to $4/3$ (see text)
• Figure 3: (Color online) Real part of the optical conductivity versus frequency, $\omega$, plotted on a log-log scale. The crossover from the $dc$ limit at very low frequencies in the bad metal to UDR around ln$(\omega)\simeq -3$ close to the Mott QCP (for $U\simeq 1.8$) is clearly seen. The $dc$ limit contribution progressively vanishes in the proximity of the Mott QCP, and UDR emerges in the quantum critical region associated with the continuous MIT.