Power-Law Spectra and Asymptotic $ω/T$ Scaling in the Orbital-Selective Mott Phase of a Three-Orbital Hubbard Model

TL;DR

This work shows that a carefully engineered three-orbital Hubbard model with a symmetry-protected node in the hybridization exhibits an orbital-selective Mott phase with robust power-law spectra at zero temperature and asymptotic $\omega/T$ scaling at finite temperature. Using single-site DMFT combined with full-density-mmatrix NRG, the authors map a $T$-$U$ phase diagram featuring metallic, coexistence, and OSM regions, and demonstrate that the OSM phase supports data-collapse scaling forms for both conduction and $f$-orbital spectra across wide ranges of $\omega/T$. They relate the scaling to a self-consistent pseudo-gap impurity problem, discuss crossover scales $T^*$ that remain finite in the OSM phase, and contrast PH-symmetric and asymmetric cases to reveal rich, orbitally selective non-Fermi-liquid dynamics. The results offer insight into how local interactions can generate scale-invariant dynamics with potential transport signatures and motivate extensions to cluster DMFT and connections to flat-band and strongly correlated materials. The findings have implications for understanding non-Fermi-liquid behavior in correlated materials and provide a framework for exploring $\,\omega/T$ scaling in optical conductivity and dc transport in realistic lattice models.

Abstract

Quantum materials whose properties lie beyond the celebrated Landau Fermi-liquid paradigm have been observed for decades across diverse material platforms. Finding microscopic lattice models for metallic states that exhibit such peculiar behavior remains a major theoretical challenge, as these features often originate from strong quantum fluctuations in strongly interacting electron systems. Here we investigate a three-orbital Hubbard model at a high-symmetry point that hosts a transition from a metallic to an orbital-selective Mott (OSM) phase. Employing single-site dynamical mean-field theory combined with full-density-matrix numerical renormalization group, we chart the $T-U$ phase diagram and obtain high-resolution real-frequency dynamics. In the OSM regime we find asymptotically scale-invariant (power-law) single-particle spectra and asymptotic $ω/T$ scaling in both charge and spin channels, spanning several decades in frequency and temperature.

Figures (7)

• Figure 1: Phase diagram and local $f$–orbital spectra across the orbital–selective Mott (OSM) transition. (a) Phase diagram in the $T$–$U$ plane showing regions I (metal), II (coexistence), and III (orbital selective insulator with power–law spectrum). (b) $f$–orbital spectra at $T=10^{-10}$ across the II$\to$III boundary, initialized from the metallic solution. (c) $f$–orbital spectra at $T=10^{-10}$ across the II$\to$I boundary, initialized from the power–law solution.
• Figure 2: $\omega/T$ scaling of single–particle spectra in the OSM phase at particle–hole symmetry. (a) $c_1$-orbital spectra plotted as $\rho_{c_1}(\omega)/\rho_0 \cdot T^{1/3}$ versus $\omega/T$ collapse onto a single curve over many decades. Guide lines highlight $|\omega/T|^{-1/3}$ at large $|\omega|/T$ and $|\omega/T|^{-1/2}$ at small $|\omega|/T$. (b) $f$-orbital spectra plotted as $\rho_{f}(\omega)/\rho_0 \cdot T^{-1/3}$ versus $\omega/T$ collapse onto a universal curve with $|\omega/T|^{+1/3}$ at large $|\omega|/T$ and a constant plateau at small $|\omega|/T$, consistent with $\rho_f(\omega=0,T)\sim T^{1/3}$. The interaction is fixed, $U=10>U_{c1}$, while colors encode temperature (blue: low $T$; red: high $T$).
• Figure 3: Local dynamical spin susceptibility in the OSM phase at particle–hole symmetry ($U=10>U_{c2}$). Temperature-dependent curves of the imaginary part of the local spin susceptibility, $\chi"_{S}(\omega,T)$, are plotted against $\omega/T$ after rescaling by $T^{\alpha}$ (an additional factor $10^{10\alpha}$ is applied for better comparison). (a) With $\alpha=\tfrac{1}{3}$, the high-frequency tail collapses and follows $\chi"_{S}\propto |\omega|^{-1/3}$ for $|\omega|/T\gg1$. (b) With $\alpha=\tfrac{1}{2}$, the low-frequency sector collapses for intermediate temperatures ($T\geq 10^{-7}$) and is linear, $\chi"_{S}\propto \omega$, for $|\omega|/T\lesssim1$. (c) With $\alpha=1$, the low-frequency sector for ultra-low temperatures ($T\leq 10^{-7}$) again shows $\chi"_{S}\propto \omega$, indicating a change in the temperature scaling exponent while preserving the linear $\omega$ dependence. Colors encode temperature (blue: low $T$; red: high $T$).
• Figure 4: $\omega/T$ scaling at particle–hole asymmetry in the OSM phase. Spectra are plotted on log–log axes using a mirrored abscissa: for $\omega<0$ we show $-\log|\omega/T|$ (hole side, left), and for $\omega>0$ we show $\log(\omega/T)$ (particle side, right). Curves are color–coded by temperature (blue: lowest $T$; red: highest $T$). (a) $f$-orbital spectrum: $T^{-1/2}\rho_f(\omega,T)$. (b) effective medium: $T^{-1/2}\!\left[-\mathrm{Im}\,\Delta(\omega,T)\right]$. (c) $c_1$-orbital spectrum: hole–side collapse for $T^{+1/2}\rho_{c_1}(\omega,T)$, and an additional particle–side low–frequency collapse for $0<\omega\lesssim T$ when plotted without a temperature prefactor (effective exponent $\alpha=0$).
• Figure 5: Single-particle spectra and dynamic spin susceptibility of the pseudo-gap SIAM. Results are shown for the spectral function (a–c) and the imaginary part of the local spin susceptibility (d–f). Panels (a,d) display data at the quantum critical point $U=U_c^\text{PSIAM}\approx 5.784$, panels (b,e) close to the QCP on the LM side with $U=7\gtrsim U_c^\text{PSIAM}$, and panels (c,f) deep in the LM phase with $U=20\gg U_c^\text{PSIAM}$. All spectra are plotted as functions of $\omega/T$ and rescaled by $T^\alpha$ with exponents $\alpha$ chosen for optimal data collapse.