Quantum Critical Transport Near the Mott Transition
Published in Phys. Rev. Lett. 107, 026401 (2011)


  "Is the paradigm of quantum criticality even a useful language to describe high temperature transport around  
  the Mott point?"

Scaling ideas and QFT are  often associated with the phenomenon of disordered-driven Anderson localization of non interacting electrons. However,  a considerable number of experiments provide compelling evidence that strong correlation effects may be the dominant mechanism of the metal-insulator transition (MIT)-- some form of Mott localization. Should one then expect similar or very different transport phenomenology in the Mott picture? 

Many systems close to the  MIT often display surprisingly similar transport features in the high temperature regime. Here, the family of resistivity curves typically assumes a characteristic ``fan-shaped'' form (Fig.  1-a), reflecting a gradual crossover: at high T resistivity depends only weakly on the control parameter, while at low T system rapidly converges towards metal or insulator.

Since temperature acts as a natural cutoff scale for the metal-insulator transition, such behavior is precisely what one expects for quantum criticality . In some cases the entire family of curves displays beautiful scaling behavior, with a remarkable ``mirror symmetry'' of the  relevant scaling functions.
Fig. 1: DMFT phase diagram of the fully frustrated half-filled Hubbard model, with a shaded region showing where quantum critical-like scaling is found. The thick  dashed line, which extends at T>Tc shows the “instability trajectory” U*(T), and the crossover temperature To delimits the QC region (dash-dotted lines). The inset shows examples of eigenvalue curves at three different temperatures, with pronounced minima at U*(T)  determining the instability line.


 "Under which microscopic conditions should one expect such scaling phenomenology? What is the corresponding 
  driving force for the transitions?"

Despite recent progress, such basic physics questions remain the subject of much ongoing controversy and debate. Moreover, they are not easy to address to because conventional Fermi liquid concepts simply cannot be utilized in the relevant high temperature incoherent DMFT-- the only theoretical method that is most reliable precisely at high temperatures.

To address the question of possible QC scaling phenomena in systems where the Mott localization is the driving force of MIT, we focus on half-filled fully-frustrated Hubbard model, and solve it within DMFT framework.
Fig. 2:  (a)  DMFT resistivity along trajectories parallel to instability trajectory in T>Tc crossover region;  (b) IPT and CTQMC data scaled by T0

 "Is it  possible to reveal any features of QPT when focusing on the model where MIT is driven purely by electron-
  electron interactions?"

To answer this question, we  performed a systematic study of incoherent transport in the high  temperature crossover region of the half-filled one-band Hubbard model.

Main results are shown in Fig. 2 and Fig. 3.

We find that the family of resistivity curves (Fig. 2-a) displays characteristic quantum critical scaling (Fig. 2-b) of the form
ρ( T , δ U ) = ρc ( T ) f (T/ T0 (δ U)), with  T0 (δ U)~|δU|zν

The corresponding beta-function
~ln(ρc/ρ )
(Fig. 3-a) displays a ``strong coupling'' form reflecting the peculiar mirror symmetry of the scaling curves (Fig. 3-b).
Fig. 3 (a) shows linear in ln behavior close to the transition. ;  Vertical dashed lines indicate the region where mirror symmetry of curves is found. (b) shows reflection symmetry of   scaled curves close to the transition.
 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.

  More details on this project can be found in our recent PRL paper.