Quantum Critical Transport near the Mott Transition

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.