Friday, July 8, 2016

Status of the fermion Hubbard model in cold atoms

A major achievement of ultra cold atoms was to simulate the Bose Hubbard model 14 years ago.
Progress towards the fermion Hubbard model (beloved in the strongly correlated electron community) has been slower. 
Cooling fermionic atoms is much more difficult.

There is a recent PRL which gives some indication of where things are at.
Observation of 2D Fermionic Mott Insulators of K40 with Single-Site Resolution 
Lawrence W. Cheuk, Matthew A. Nichols, Katherine R. Lawrence, Melih Okan, Hao Zhang, and Martin W. Zwierlein

The figure below shows the measured local magnetic moment as a function of temperature. The upper curve is at half filling and the bottom for a strongly doped system. The solid lines are theoretical curves obtained from high temperature series expansions.
The temperature is scaled by the hopping integral t in the Hubbard model.

The authors note they have reached entropies as low as k_B.

Although this is significant progress it should be noted that these are still very high temperatures from a solid state physics perspective. For the high T_c cuprate superconductors, these temperatures correspond to tens of thousands of Kelvin, two orders of magnitude about the superconducting transition temperature.

On a more promising note, there is interesting physics to access in the Hubbard model at temperatures of order of some fraction of t and at entropies of order k_B . ln(2).
These are the characteristic scales of the bad metal regime.
A particularly interesting experiment would be to measure the viscosity in this regime and see whether it violates the conjectured quantum limits.

I thank my UQ colleague, Matt Davis for stimulating my interest in these issues.

Update. August 1, 2016
Thierry Giamarchi has a helpful commentary at the Journal Club for Condensed Matter Physics on two recent preprints that report similar experiments from two other groups.

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