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arXiv:1906.05293 · Physical review. B./Physical review. B

Mott quantum criticality in the one-band Hubbard model: Dynamical mean-field theory, power-law spectra, and scaling

Heike Eisenlohr, Seung‐Sup B. Lee, Matthias Vojta C

Published Oct 31, 2019• 27 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.100.155152

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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.
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.
We study electric transport near the Mott metal-insulator transition. Optical conductivity of the half-filled Hubbard model on a triangular lattice is calculated based on a cellular dynamical mean field theory including vertex corrections inside the cluster. By investigating the spectrum at low frequencies, we find that a Drude peak on the metallic side smoothly connects to an "ingap" peak on the insulating side. The optical weight of these peaks exhibits a critical behavior with power-law near the Mott critical end point, ∣D−D∗∣∝∣U−U∗∣1/δ|D-D^*|\propto|U-U^*|^{1/δ}∣D−D∗∣∝∣U−U∗∣1/δ. We find that the critical exponent 1/δ1/δ1/δ differs from the exponents in the thermodynamics.
Abstract We present a T = 0 K renormalization group (RG) phase diagram for the hole-doped 2D Hubbard model on the square lattice. The RG method employed is nonperturbative in treating quantum fluctuations of the single-particle occupation number via the unitarily decoupling of one electronic state at every RG step. As a result, the RG phase diagram possesses the quantum fluctuation energy scale (ω) as one of its axes. Using effective Hamiltonians and wavefunctions for the low-energy many-body eigenstates for the doped Mott liquid obtained from the stable fixed point of the RG flows, we demonstrate the collapse of the pseudogap for charge excitations (Mottness) at a quantum critical point (QCP) possessing a nodal non-Fermi liquid with superconducting fluctuations, and spin-pseudogapping near the antinodes. The QCP is characterised using both thermodynamic and quantum information-theoretic measures. d-wave superconducting order is shown to arise from this quantum critical state of matter. The pseudogap phase possesses a variety of fluctuations that lead to several symmetry-broken phases at low-energies. Benchmarking of the ground state energy per particle and the double-occupancy fraction obtained from a finite-size scaling analysis against existing numerical results yields excellent agreement. We present detailed insight into the T = 0 origin of several experimentally observed findings in the cuprates, including Homes law and Planckian dissipation. We also establish that the heirarchy of temperature scales for the pseudogap (T PG), onset temperature for pairing (T ons), formation of the Mott liquid (T ML) and superconductivity (T C) obtained from our analysis is quantitatively consistent with that observed experimentally for some members of the cuprates. Our results offer insight on the ubiquitous origin of superconductivity in doped Mott insulating states, and pave the way towards a systematic search for higher superconducting transition temperatures in such systems.
We perform a systematic study of incoherent transport in the high temperature crossover region of the half filled one-band Hubbard model. We demonstrate that the family of resistivity curves displays characteristic quantum critical scaling of the form $\ensuremath{\rho}(T,\ensuremath{\delta}U)={\ensuremath{\rho}}_{c}(T)f\mathbf{(}T/{T}_{0}(\ensuremath{\delta}U)\mathbf{)}$, with ${T}_{0}(\ensuremath{\delta}U)\ensuremath{\sim}|\ensuremath{\delta}U{|}^{z\ensuremath{\nu}}$, and ${\ensuremath{\rho}}_{c}(T)\ensuremath{\sim}T$. The corresponding $\ensuremath{\beta}$ function displays a ``strong coupling'' form $\ensuremath{\beta}\ensuremath{\sim}\mathrm{ln}({\ensuremath{\rho}}_{c}/\ensuremath{\rho})$, reflecting the peculiar mirror symmetry of the scaling curves. This behavior, which is surprisingly similar to some experimental findings, indicates that Mott quantum criticality may be acting as the fundamental mechanism behind the unusual transport phenomena in many systems near the metal-insulator transition.
The experimentally established phase diagram of the half-filled Hubbard model features the existence of three distinct finite-temperature regimes, separated by extended crossover regions. A number of crossover lines can be defined to span those regions, which we explore in quantitative detail within the framework of dynamical mean-field theory. Most significantly, the high-temperature crossover between the bad metal and Mott-insulator regimes displays a number of phenomena marking the gradual development of the Mott insulating state. We discuss the quantum critical scaling behavior found in this regime, and propose methods to facilitate its possible experimental observation. We also introduce the concept of quantum Widom lines and present a detailed discussion that highlights its physical meaning when used in the context of quantum-phase transitions.