Obviously we should try to finish this project off. I will now
give it my prompt attention. Below are comments.
In any case, I am very pleased by the agreement between your QMC data and
our DMFT data for the cubic lattice evident in the attached figure. In
fact, I would assume that most of the disagreement might be due to
discretization errors in the QMC data. Do you agree?
The agreement is very nice. Certainly there are some Trotter errors in
our results. I think I sent some files to you for different Delta tau.
As an example, for U=8 we had
dtau=0.125 dtau=0.083
beta T D D
1.00000 1.00000 0.05113 0.0531
2.00000 0.50000 0.04292 0.0452
4.00000 0.25000 0.04540 0.0482
Our data gets shifted up towards yours. Should I do an extrapolation,
do you think? If I just us the two dtau values I have, it would be
a bit careless. I really should run 4-5 dtau values to get a
fit/extrapolation that we can be confident about. It would take a
few days or a week to do the jobs. No big problem.
Unfortunately, we do not really understand your NN spin correlation data,
especially the weak deviations from 1/T dependences and the independence of
U at large T. We could find the expected relations between this
correlation data and the AF-induced enhancement in D only by making
shifting your data in unreasonable ways.
Did this issue ever get resolved? If you think it is a problem with our
data, then I would like to look at it carefully. I believe (of course!)
that our code is correct, so it must be the finite size of our lattice,
or Trotter errors, or something like that. As you know, the optical
lattice experimentalists will presumably go after the NN spin correlation
now that they have focussed on D. It will be a while before they
get to T low enough for long range order. So, it is probably very worth
while for us to get good understanding of what will be their next target.
Incidentally, did Thereza send adequate 2D NN spin correlation data?
As you know, I also have a lot tucked away in files. Do I need
to dig it out and send it?
By the way, we just had Jan Kunes as a visitor who mentioned a DMFT-QMC
comparison for the triangular lattice done in collaboration with you.
This lattice type could also be relevant for our comparison; however, the paper
does not contain double occupancies. I think that a comparison between square
and triangular lattices could even be relevant experimentally, because
the differences could essentially be attributed to AF fluctuations
present only on the square lattice.
If you would like triangular lattice data I can easily get it. What U and
T values are you interested in? (Thereza- unless you are super eager to,
why don't you just let me generate this data so you can focus on the 3D
data for Nandini and MOhit?)
So... what is the next step? Start writing? Again, I will respond to
emails on this project rapidly from this point onwards.
Dear Nils,
I attach plots of the nn spin correlation and double occupancy for 3D
hubbard at half filling. The double occupancy plot contains both
data from my runs (indicated by "rts") and Thereza. Again, Thereza
has more data for other U values (up to at least U=9).
You can see my nn spin correlation data is getting noisy at low T.
There is one data point in particular at U=6 and T=0.25 that looks
nutty.
Again, I will look up the 2D nn spin correlation data from my files.
We should discuss what you see this paper as covering.
Richard Scalettar
Professor and Vice Chairman, Physics Department
University of California, Davis 95616
phone 530-554-1605
fax 530-752-4717
email scalettar@physics.ucdavis.edu
http://leopard.physics.ucdavis.edu/rts/<nupndn3.ps><c10vsT1.ps>
Nils Blümer
Institut für Physik, KOMET 337 Room: 03 134, Staudingerweg 7
Johannes Gutenberg-Universität Phone: (+49) 6131 / 392 22 77
55099 Mainz, Germany FAX: (+49) 6131 / 392 09 54
http://komet337.physik.uni-mainz.de/Bluemer/