Quantum Critical Transport near the Mott Transition

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 $\rho (T,\delta U)={\rho }_c(T)f\mathbf{(}T/T_0(\delta U)\mathbf{)}$, with $T_0(\delta U)\sim |\delta U{|}^{z\nu }$, 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.

Figure 1

(a) DMFT resistivity curves as a function of temperature along different trajectories $-0.2\le \delta U\le +0.2$ with respect to the instability line $\delta U=0$ (black dashed line; see the text). Data are obtained by using IPT impurity solver. (b) Resistivity scaling; essentially identical scaling functions are found from CTQMC (open symbols) and from IPT (closed symbols).

Figure 2

DMFT phase diagram of the fully frustrated half filled Hubbard model, with a shaded region showing where quantum critical-like scaling is found. Metallic $U_{c2}(T)$ and insulating $U_{c1}(T)$ spinodals (dotted lines) are found at $T<T_c$; the corresponding first-order phase transition is shown by a thick solid line. The thick dashed line, which extends at $T>T_c$, shows the instability trajectory $U^{\star }(T)$, and the crossover temperature $T_0$ delimits the QC region (dash-dotted lines). The inset shows examples of eigenvalue curves at three different temperatures, with pronounced minima at $U^{\star }(T)$ determining the instability trajectory.

Figure 3

(a) Scaling parameter $T_0(\delta U)$ as a function of control parameter $\delta U=U-U^{\star }$; the inset illustrates power-law dependence of scaling parameter $T_0=c|\delta U{|}^{z\nu }$. (b) Resistivity ${\rho }_c(T)$ of the separatrix. Excellent agreement is found between IPT (closed symbols) and CTQMC (open symbols) results.

Figure 4

(a) The $\beta$ function shows linear in $\ln ({\rho }_c/\rho )$ behavior close to the transition. Open symbols are for the metallic branch ($\delta U<0$), and closed ones are for the insulating side ($\delta U>0$); vertical dashed lines indicate the region where mirror symmetry of curves is found. (b) Reflection symmetry of scaled curves close to the transition.