Dear Richard,
sorry for the long delay. We had some stability issues with the DMFT runs for triangular lattices in the AF phase and are still not sure whether we can reach the required precision; of course, it wouldn´t make sense to ask for direct costly QMC comparison runs when we don´t have the corresponding DMFT data. Furthermore, I am now less confident that we can learn much from extending our comparison to the triangular case, since already the paramagnetic results for D deviate significantly from those for cubic lattices (with the same coordination number).
On 24.08.2010, at 19:39, Richard T. Scalettar wrote:
Dear Elena and Nils,
Thereza and I would like to finish off whatever runs would be useful
for our joint project. Can you please let us know precisely what would
be useful to you? Below is a summary of what we have sent in the past
(everything is at half-filling). I apologize for the review, but I
wanted to try to remember what had already been done before discussing
new runs.
==================================================================
In 2D, I sent double occupation data for 8x8 lattices and
U=8, 10, 12, 15 for T=0.1 to T=10. For U=8,10,15 I sent data for
two different delta tau values.
Here is my wishlist:
# U delta_tau old delta_tau new
8 0.0833, 0.125 0.0625, 0.167
10 0.0833, 0.125 0.0625, 0.167
12 0.0833 0.0625,0.125,0.167
15 0.05, 0.0625 0.0833,0.125
In 3D, I sent double occupation for U= 2,4,6,8,12 and T=0.1 to T=20. I
only sent results for one delta tau value, but several lattice sizes,
from 4^3 to 8^3. I also sent nn spin correlations for 8x8x8 lattices
and T=0.20 to T=4.0 and U=4,6,8,12.
It would be great to see at least one more discretization value for U=12 and U=8, but only if the cost is reasonable.
Meanwhile, Thereza sent 2D data for the double occupation and spin
correlations and structure factor for U=2,4,6,8 on 10x10 lattices
at dtau=0.125.
At the moment, I cannot find some of this data; we will probably have to reextract the files from posu.opj (sent by Thereza on June 6) and convert to a common format and naming scheme. Frankly, I cannot make sense of most of the columns , e.g., in \\omnis\tclp\davis\afl10u8n1.dat in posu.opj.
Could you maybe help us with extracting D and the NN correlations for U=8, so that we can compare to the 8x8 data and quantify finite-size effects?
However, I do have a file "n1l10u9.dat" with the content
4 0.00391 64 -0.11027 9.5E-5 -0.03122 1E-6 0.24122 1.1E-5
4 0.00781 32 -0.22002 1.68E-4 -0.06226 6E-6 0.23247 1.9E-5
4 0.01563 16 -0.43619 2.48E-4 -0.12312 1.6E-5 0.21521 2.9E-5
4 0.03125 8 -0.84173 6.01E-4 -0.23593 8E-5 0.18269 7.4E-5
4 0.0625 4 -1.49178 5.7E-4 -0.40806 2.3E-4 0.12959 8.4E-5
4 0.125 2 -2.19533 5.85E-4 -0.57673 5.25E-4 0.07015 6.7E-5
6 0.125 1.33333 -2.43827 6.54E-4 -0.6194 5.69E-4 0.0479 6.6E-5
8 0.125 1 -2.54201 8.81E-4 -0.6419 0.00113 0.03888 5.3E-5
12 0.125 0.66667 -2.63201 0.00108 -0.67985 0.00133 0.03309 6.1E-5
16 0.125 0.5 -2.68269 0.00112 -0.72636 0.00145 0.03263 9.7E-5
24 0.125 0.33333 -2.74058 0.0017 -0.79886 0.0023 0.03425 9E-5
32 0.125 0.25 -2.78221 0.00142 -0.85507 0.00191 0.0359 1.41893E-4
40 0.125 0.2 -2.80992 0.00208 -0.89489 0.00271 0.03722 7.7464E-5
48 0.125 0.2 -2.82584 0.00183 -0.91795 0.00232 0.03801 7.76299E-5
64 0.125 0.2 -2.83706 0.0017 -0.93424 0.00239 0.03858 8.327E-5
which we extracted from nils.opj (sent by Thereza on April 30); I think it represents U=9 on a 10x10 lattice. Qualitatively, it seems to show exactly the feature I have looking for (enhancement of D proportional to NN correlations).
I would be extremely interested in corresponding data for other discretizations, e.g., dtau=0.0833 and 0.167.
She also sent U=0.1 results on 10x10 and 14x14 lattices.
I must have overlooked this data. It is really nice since it shows that (i) finite-size effects are negligible for beta<2.5 and reach about 1.5% at the low-T plateau and that (ii) the plateau value -0.08 is indeed much closer to the noninteracting limit (of 0).
In 3D, Thereza sent double occupations at U=6, 9 for 4^3, 6^3 and 8^3
at dtau=0.125. She also has run 4^3, 6^3 and 8^3 for 2<T<5
at different dtau, but has not sent the data yet.
==================================================================
Okay, so now please tell us what you would like. What geometry (square,
cubic, triangular)? What U, T? Do you want us to extrapolate to dtau=0
and, (if possible) lattice size = infty?
Again, I think we should concentrate on the square lattice until we have definite results there.
It would be great to get this all done before Nils visits in October.
Perhaps we can even have a draft of a paper that we can discuss when he
is here.
Richard
cc: Thereza
Best regards
Nils
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/