Universal Mott quantum criticality in a modified periodic Anderson model

TL;DR

The paper investigates universal Mott quantum criticality in the modified periodic Anderson model (MPAM) using dynamical mean-field theory with numerical renormalization group impurity solving. It demonstrates a zero-temperature quantum critical point with robust ω/T scaling in single- and two-particle correlators and identifies a quantum-critical region defined by a vanishing crossover scale, along with distinctive optical and DC transport signatures. The resistivity exhibits a data-collapse scaling form with ν z on the metallic and insulating sides, yielding exponents that closely match those found in the single-band Hubbard model, suggesting a common universality class for Mott quantum criticality. The results position MPAM as a canonical, higher-dimensional platform for exploring genuine Mott quantum criticality and its universal transport fingerprints, with explicit signatures such as isosbestic points in optical conductivity and a MIR peak that minimizes at the QCP.

Abstract

Mott quantum criticality is a central theme in correlated electron physics, observed in systems featuring both continuous zero-temperature transitions and those with finite-temperature critical endpoints. Within dynamical mean-field theory (DMFT), the paradigmatic single-band Hubbard model (SBHM) displays such criticality only above a finite-temperature endpoint. In contrast, the modified periodic Anderson model (MPAM) is a rare example known to host a surface of genuinely continuous Mott quantum critical points (QCPs) at zero temperature. Using DMFT with the numerical renormalization group as an impurity solver, we investigate the finite-temperature, real-frequency properties of the MPAM. Our central finding is the emergence of quantum critical scaling in the electrical resistivity, with critical exponents $z_{\text{met}} = 0.76$ and $z_{\text{ins}} = 0.66$ on the metallic and insulating sides, respectively. These values fall within the range reported for the SBHM, suggesting that both transitions are governed by a common universality class. We further substantiate the presence of local quantum criticality by demonstrating robust $ω/T$ scaling in single- and two-particle correlation functions. Finally, we identify novel transport signatures in the optical conductivity, where the distinct evolution of two isosbestic points serves as a unique fingerprint of the QCP. These results establish the MPAM as a canonical model for investigating genuine Mott quantum criticality and support the existence of a universal framework for this fundamental phenomenon.

Figures (9)

• Figure 1: (Top) Rescaled spectral weight, $\text{A}_{\text{f}}(\omega)V^2/t_{\perp}^2$, as a function of $\omega t_{\perp}^2/ZV^2$ at $T=10^{-3}$. (Bottom) Energy scales: quasi-particle weight (${Z}$)(solid lines- red), crossover scale(dashed-blue) and Mott gap ($\Delta_g$)(solid lines- black) vs. inter-orbital coupling $t_\perp$. The crossover scale is extracted from the self-energy deviation from the power-law form(see text corresponding to Fig. \ref{['fig:self_energy_wm']}). $Z$ and $\Delta_g$, calculated at $T=0$, vanish with exponents $2.0$ and $1.05$. Inset: $\text{A}_{\text{f}}(\omega)$ for different $t_\perp$. Parameters used: $U=1.75$.
• Figure 2: -Im$\Sigma_{\text{f}}(\omega)$ is plotted for different inter-orbital coupling, $t_\perp$ at a temperature $T=0.001$. We can observe a gradual influence of the power-law as we approach the QCP. Parameters used: $U=1.75$.
• Figure 3: (top)Imaginary part of the self-energy, $-\Sigma_{\text{f}}(\omega)$ and (bottom)spectral function, $\text{A}_{\text{f}}(\omega)$, are plotted for different $\beta$'s at the QCP. We can observe $\omega/T$ scaling in both of them with exponents $=0.36 \,(\text{A}_{\text{f}}(\omega)),-0.36\,(\text{Im}\Sigma_{\text{f}}(\omega))$. (Inset) shows the plot of unscaled $A(\omega)$ vs. $\omega$. Parameters used: $U=1.75$.
• Figure 4: Scaling plot of the dynamical susceptibility, $T^{0.36}\chi"(\omega,T)$, shown for several temperatures ($\beta$ ranging from 50 to 1000). (a) At the quantum critical point ($t_{\perp} = t_{\perp,c} = 1.033$), the data collapse onto a universal curve over three decades, consistent with quantum critical scaling glossop2011critical. (b, c) Away from the QCP, for $t_\perp = 0.7$ (top right) and $t_\perp = 1.1$ (bottom right), the scaling collapse clearly fails. Parameters used: $U=1.75$.
• Figure 5: (top) Optical conductivity plotted for various inverse temperatures $\beta$ at $t_\perp = 0.7$. The inset shows two isosbestic points located before and after the MIR peak. (bottom) Optical conductivity plotted for $t_\perp = 1.033$ (top) and $1.08$ (bottom). At the QCP, the conductivity $\sigma(\omega)$ follows a power-law behavior, as indicated by the dashed maroon line, with an exponent of $0.737$, which is approximately $2r$, where $r = 0.36$ is the critical exponent kksujan2023emergent. Parameters used: $U=1.75$.