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arXiv:1012.5833 · Physical Review Letters

Quantum Critical Transport near the Mott Transition

Hanna Terletska, J. Vučičević, D. Tanasković, V. Dobrosavljević

Published Jul 5, 2011• 132 citations
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Abstract

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.

DOI
10.1103/physrevlett.107.026401

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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 \ensuremathρ(T,\ensuremathδU)=\ensuremathρc(T)f(T/T0(\ensuremathδU))\ensuremath{\rho}(T,\ensuremath{\delta}U)={\ensuremath{\rho}}_{c}(T)f\mathbf{(}T/{T}_{0}(\ensuremath{\delta}U)\mathbf{)}\ensuremathρ(T,\ensuremathδU)=\ensuremathρc​(T)f(T/T0​(\ensuremathδU)), with T0(\ensuremathδU)\ensuremath∼∣\ensuremathδU∣z\ensuremathν{T}_{0}(\ensuremath{\delta}U)\ensuremath{\sim}|\ensuremath{\delta}U{|}^{z\ensuremath{\nu}}T0​(\ensuremathδU)\ensuremath∼∣\ensuremathδU∣z\ensuremathν, and \ensuremathρc(T)\ensuremath∼T{\ensuremath{\rho}}_{c}(T)\ensuremath{\sim}T\ensuremathρc​(T)\ensuremath∼T. The corresponding \ensuremathβ\ensuremath{\beta}\ensuremathβ function displays a ``strong coupling'' form \ensuremathβ\ensuremath∼ln(\ensuremathρc/\ensuremathρ)\ensuremath{\beta}\ensuremath{\sim}\mathrm{ln}({\ensuremath{\rho}}_{c}/\ensuremath{\rho})\ensuremathβ\ensuremath∼ln(\ensuremathρc​/\ensuremathρ), 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.
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We study electric transport near the Mott metal-insulator transition in a triangular-lattice Hubbard model at half filling. We calculate optical conductivity $\ensuremath{\sigma}(\ensuremath{\omega})$ based on a cellular dynamical mean-field theory including vertex corrections inside the cluster. Near the Mott critical end point, a Drude analysis in the metallic region suggests that the change in the Drude weight is important rather than that in the transport scattering rate for the Mott transition. In the insulating region, there emerges an ``in-gap'' peak in $\ensuremath{\sigma}(\ensuremath{\omega})$ at low $\ensuremath{\omega}$ near the Mott transition, and this smoothly connects to the Drude peak in the metallic region with decreasing Coulomb repulsion. We find that the weight of these peaks exhibits a power-law behavior upon controlling Coulomb repulsion at the critical temperature. The obtained critical exponent suggests that conductivity does not correspond to magnetization or energy density of the Ising universality class in contrast to several previous works.
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We study charge transport across the metal-insulator crossover in the half-filled two-dimensional Hubbard model, with particular emphasis on precision control. The dynamic current-current correlation function is obtained directly in the thermodynamic limit, and the optical conductivity is extracted using numerical analytic continuation. To achieve this, we develop a multiscale approach: the non-perturbative low-frequency behavior is computed using the unbiased diagrammatic Monte Carlo technique, while the high-frequency physics is captured via a self-consistent (semi-)analytic diagrammatic theory. We found that across a broad temperature range where the DC resistivity displays anomalous scaling, ∼Tα\sim T^α∼Tα with 0<α≲10<α\lesssim 10<α≲1, the Nernst-Einstein relation implies the diffusion constant with the characteristic ∼1/T\sim 1/\sqrt{T}∼1/T​ "strange metal" behavior. It was also revealed that the insulating regime is entered through a peculiar non-Fermi liquid state-which we call a Pseudogap Metal-characterized by insulating charge compressibility coexisting with metallic transport. Diagrammatically, the high-temperature incoherent transport is captured by the dressed polarization bubble, whereas near the metal-insulator crossover, the effective interaction vertex between opposite-spin particles is responsible for transferring the Drude weight to a high-frequency continuum.