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arXiv:2509.23758 · SciPost Physics

Power-law spectra and asymptotic $\omega/T$ scaling in the orbital-selective Mott phase of a three-orbital Hubbard model

Fabian Eickhoff

Published Feb 19, 2026• 1 citation
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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 T – U 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 \omega/T ω / T scaling in both charge and spin channels, spanning several decades in frequency and temperature.

DOI
10.21468/scipostphys.20.2.050

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Power-law spectra and asymptotic ω/T\omega/Tω/T scaling in the orbital-selective Mott phase of a three-orbital Hubbard model
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 T – U 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 \omega/T ω / T scaling in both charge and spin channels, spanning several decades in frequency and temperature.
Recent studies of electrical transport, both theoretical and experimental, near the bandwidth-tuned Mott metal-insulator transition have uncovered apparent quantum critical scaling of the electrical resistivity at elevated temperatures, despite the fact that the actual low-temperature phase transition is of first order. This raises the question whether there is a hidden Mott quantum critical point. Here we argue that the dynamical mean-field theory of the Hubbard model admits, in the low-temperature limit, asymptotically scale-invariant (i.e., power-law) solutions, corresponding to the metastable insulator at the boundary of the metal-insulator coexistence region; these solutions can be linked to the physics of the pseudogap Anderson model. While our state-of-the-art numerical renormalization-group calculations reveal that this asymptotic regime is restricted to very small energies and temperatures and hence is difficult to access numerically, we uncover the existence of a wide crossover regime where the single-particle spectrum displays a different power law. We show that it is this power-law regime, corresponding to approximate local quantum criticality, which is continuously connected to and responsible for the apparent quantum critical scaling above the classical critical end point. We connect our findings to experiments on tunable Mott materials.
Quantum orbital-selective Mott (OSM) transitions are investigated within dynamical mean-field theory based on a two-orbital Hubbard model with different bandwidth at half filling. We find two distinct OSM phases both showing coexistence of itinerant electrons and localized spins, dependent on whether the Hund's coupling is full or of Ising type. The critical values and the nature of the OSM transitions are efficiently determined by entanglement entropy. We reveal that vanishing of the Kondo energy scale evidenced by absence of local spin fluctuations at low frequency in local dynamical spin susceptibility is responsible for the appearance of non-Fermi-liquid OSM phase in Ising Hund's coupling case. We argue that this scenario can also be applied to account for emergent quantum non-Fermi liquid in the one-band Hubbard model when short-range antiferromagnetic order is considered.
While a specific kind of strange metal is increasingly found to be the "normal" states in a wide variety of unconventional superconductors, its microscopic origin is presently a hotly debated enigma. Using dynamical mean-field theory (DMFT) based on hybridization expansion of continuous-time quantum Monte-Carlo (CTQMC) solver for an extended two-band Hubbard model (2BHM), we investigate the conditions underlying the emergence of such a metal. Specifically, we tie strange metallicity to an orbital-selective Mottness in 2BHM or momentum-selective Mott phase (OSMP) in 2D Hubbard models inspired by a cluster-to-orbital mapping. We find (i)(i)(i) disparate spin and charge responses, (ii)(ii)(ii) fractional power-law behavior and ω/Tω/Tω/T-scaling in the charge and spin fluctuation responses, and (iii)(iii)(iii) very good accord with optical conductivity and nuclear magnetic relaxation rates in the slightly underdoped normal states of cuprates and Fe-arsenides. We analyze the local problem using bosonization to show that such anomalous responses arise from a lattice orthogonality catastrophe specifically in the OSMP. Our work establishes the intimate link between strange metallicity and selective Mottness in quantum matter.
Finding microscopic models for metallic states that exhibit quantum critical properties is a major theoretical challenge. We calculate the dynamical local spin susceptibility $\ensuremath{\chi}(T,\ensuremath{\omega})$ for a Hubbard model at half-filling using dynamical mean-field theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite-temperature critical point. The signature of the latter is $\ensuremath{\omega}/T$ scaling, where $\ensuremath{\omega}$ is the frequency and TTT is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity, and they are relevant to experiments on organic charge-transfer salts.
Using the density matrix renormalization group technique we study the effect of spin-orbit coupling on a three-orbital Hubbard model in the (t2g)4{({t}_{2g})}^{4}(t2g​)4 sector and in one dimension. Fixing the Hund coupling to a robust value compatible with some multiorbital materials, we present the phase diagram varying the Hubbard UUU and spin-orbit coupling $\ensuremath{\lambda}$, at zero temperature. Our results are shown to be qualitatively similar to those recently reported using the dynamical mean-field theory in higher dimensions, providing a robust basis to approximate many-body techniques. Among many results, we observe an interesting transition from an orbital-selective Mott phase to an excitonic insulator with increasing $\ensuremath{\lambda}$ at intermediate UUU. In the strong UUU coupling limit, we find a nonmagnetic insulator with an effective angular momentum $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}\ensuremath{\ne}0$ near the excitonic phase, smoothly connected to the $\ensuremath{\langle}{({\mathbf{J}}^{\mathrm{eff}})}^{2}\ensuremath{\rangle}=0$ regime. We also provide a list of quasi-one-dimensional materials where the physics discussed in this paper could be realized.