Quantum Critical Transport Near the Mott Transition

TL;DR

This paper investigates quantum critical scaling of resistivity in the Hubbard model near the Mott transition, revealing universal behavior and a strong coupling beta-function that may explain anomalous transport in correlated materials.

Contribution

It demonstrates quantum critical scaling in resistivity and identifies a strong coupling beta-function near the Mott transition, linking theory to experimental observations.

Findings

Resistivity exhibits quantum critical scaling form.

The beta-function shows a strong coupling logarithmic behavior.

Scaling curves display mirror symmetry, indicating universal behavior.

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 $\rho(\delta U,T)=\rho_{c}(T)f(T/T_{o}(\delta U))$, with $T_{o}(\delta U)\sim\delta U^{z\nu}$, and $\rho_{c}(T)\sim T$. The corresponding $\beta$-function displays a "strong coupling" form $\beta\sim\ln(\rho_{c}/\rho)$, 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.