## Monday, November 7, 2016

### A concrete example of a quantum critical metal

I welcome comments on this preprint.

Quantum critical local spin dynamics near the Mott metal-insulator transition in infinite dimensions Nagamalleswararao Dasari, N. S. Vidhyadhiraja, Mark Jarrell, and Ross H. McKenzie
Finding microscopic models for metallic states that exhibit quantum critical properties such as $\omega/T$ scaling is a major theoretical challenge. We calculate the local dynamical spin susceptibility $\chi(T,\omega)$ for a Hubbard model at half filling using Dynamical Mean-Field Theory, which is exact in infinite dimensions. Qualitatively distinct behavior is found in the different regions of the phase diagram: Mott insulator, Fermi liquid metal, bad metal, and a quantum critical region above the finite temperature critical point. The signature of the latter is $\omega/T$ scaling where $T$ is the temperature. Our results are consistent with previous results showing scaling of the dc electrical conductivity and are relevant to experiments on organic charge transfer salts.
Here is the omega/T scaling, which I think is quite impressive.
We welcome comments.

#### 2 comments:

1. Hi Ross, I hope this is not a trivial question but I am not very familiar with non-finite Hubbard calculations. Is it possible to make a connection between your phase diagram and the pairing gap found in finite Hubbard systems? For instance Tsai/Kievelson finds a pairing gap in a broad region around U/t=8 (http://dx.doi.org/10.1103%2FPhysRevB.77.214502). From what I understand pairing mechanisms like this are hoped to be the basis of the high TC superconductivity in cuprates. Yet this region is Mott insulating in your phase diagram. Is there a way to relate the results of these two approaches? Thanks - and I really appreciate your blog. Just found it recently and it is very good.

1. Thanks for the question.

There are important differences between our Hubbard model and theirs. Ours is homogenous (all the t hoppings are the same), at half filling, and we solve in the infinite-dimensional limit. Theirs has in homogenous t, is not at half filling, and is two-dimensional. this is why the phase diagrams are different.