Dear Richard,
thank you very much! This is really extremely useful data for us.
Attached is a comparison of our rescaled QMC data (red) with your data (blue, dashed); here, the U=8 set is from your recent PRL while the thicker and thinner lines/symbols for U=10 are for dtau=0.0833 and dtau=0.125, respectively. The green long-dashed lines are DMFT data calculated for the paramagnetic phase on the square lattice (thin dtau=0.1, thick: extrapolated to dtau=0); the corresponding AF data (squares) is still preliminary and incomplete.
As you can see, the agreement at T>0.5 is even much better for U=10 than for U=8. This looks promising to me.
On 02.05.2010, at 20:47, <scalettar@physics.ucdavis.edu>
<scalettar@physics.ucdavis.edu> wrote:
Dear Nils,
I finished the dtau=0.0833 runs (still 8x8 lattices). I'm afraid
the Trotter errors seem to be shifting us away from your 0.025
minimum. Agreement would be worse after the extrapolation to
dtau=0.
These slight differences do not worry me at all. I mean, nobody would have expected any sort of agreement with DMFT in 2 dimensions.
It's possible finite lattice size corrections woul
affect the results further. I will not do these at the present,
however, since I am not sure with what level of precision you really
want to do the comparison.
I think we should first verify the trends without investing too much human and computer time and then decide about accuracies.
dtau 0.125 0.0833
Dmin 0.02512 0.02695
D(T=0) 0.03186 0.03501
rise 27% 30%
I find this encouraging: the relative enhancement goes up, in particular relative to the "paramagnetic behavior" (within DMFT). In fact D(T=0) might extrapolate pretty exactly to the (extrapolated to dtau=0 and rescaled) DMFT value, i.e. to about 0.038. Of course, the fact that the enhancement of D sets in at larger T in your data is a significant modification of the DMFT scenario. But such a trend would be good for experimentalists if also present in 3D.
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/<nupndnU10avg.ps><nupndnU10dt0833avg.dat>
I would be most interested in comparisons at U=8 with similar statistical accuracy (why are the error bars in the PRL data so large?) and, if possible, also for larger U, e.g. U=12 and U=15. I do not think that we need larger lattices.
I think we are steering towards a joint publication (which should include, on our side, Elena and myself). Do you agree?
Best regards
Nils
PS: Greetings also from Karsten Held (who I am just visiting in Vienna)!
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/
