Dear Theresa,
thanks for the data which looks great (see attached figures): for U=12t we have perfect agreement between the extrapolated QMC and DMFT data. In addition, there is absolutely no significant difference between the 8x8x8 results (for Dt=0.0625) and the 6x6x6 data that Elena interpolated for this discretization! So you/are were absolutely right!
For U=4t we have very good agreement QMC-DMFT at T<T_N and the expected deviations above (but even less than between DMFT and DCA). So no surprises here, but it will be nice to show this kind of agreement.
How about stronger couplings? Do you plan to do calculations at U=15t and/or U=18t? Probably one interaction is enough to see the trend.
Since we have so nice extrapolated QMC data now, we would prefer to do at least rough corrections also for the rest of the data. For this, we would need to know how the discretization values evolve towards higher T in the 8x8x8 data that we got from Richard from the nominal values
U=4 dt=0.125
U=6 dt=0.125
U=8 dt=0.0833
U=12 dt=0.0625
Of course it would be more straightforward to have 3 discretization values for all U also for T>0.5; however, since we already know the correct answer from DCA, this would not be worth considerable trouble.
By the way, I concentrated my research last week on getting the DMFT entropy curve S(T) for U/T=150, in order to compare with the data shown in the recent deLeo preprint (Fig 12, I believe). It is really challenging to get convergence along the mu-dependent Neel curve with the required precision, but I am confident to show that the DMFT results recover the correct results at low T (while they are incorrectly pinned to log 2 above T_N^DMFT). Once this curve is known, we could also compare QMC-DMFT as a function of entropy instead of temperature.
Best regards, Nils
On 03.11.2010, at 20:14, Thereza Cristina de Lacerda Paiva wrote:
Dear Nils,
I had already set some U=4 jobs when you realized U=4 was not so interesting (your plots really show TC is the same only for this U), but
I decided to keep the jobs running, just in case. I am sending files with the double occupation for 2 < beta <8 and different delta tau.
I am also sending double occupation data for U=12 and 2 < beta < 5 (or 6 in some cases) and different dtau.
All data are for 6^3 lattices. For U=12 I expect finite size effects to be really small (smaller than for U=6, which seemed small enough). This might not be the case for U=4, let me know if you think it is worth looking at that.
Let me know if you want anything else.
best,
Thereza
On Fri, 29 Oct 2010, Nils Bluemer wrote:
Dear Thereza,
yesterday I overlooked one important fact: for U<6t (and certainly for
U=4t), the DMFT Neel temperature is essentially exact, so it is not
really unexpected to find agreement between DMFT and QMC features in this range.
Attached you find a first version of the kind of plot I had in mind for
discussing energy scales. Here, the density plots measure more or less
the "flatness" of D as a function of T, i.e. indicate the positions and
widths of extrema. Obviously it would be interesting to see whether the
yellow feature visible in the QMC curve for U=12 moves downwards when
increasing U/t to 15 or 18. So strong coupling seems most interesting now (including, maybe a second discretization for U/t=12).
By the way, if computer time is a concern, we could help out (with up
to 200 recent Xeon E5410 and E5520 cores in a Debian Linux cluster).
Bests, Nils
PS: Thanks a lot also for the correlation data. It is good to see that both discretization and finite-size errors are so small, at least at U=6t. We spent quite some time playing around with the data. Unfortunately, so far our only physical conclusion is that the correlation function is surprisingly featureless.
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/
