Subject: D(T) U=8,10,12,15
From: <scalettar@physics.ucdavis.edu>
Date: Tue, 11 May 2010 11:34:31 -0700
To: <nbluemer@uni-mainz.de>, <gorelike@uni-mainz.de>
CC: "Richard T. Scalettar" <rts@physics.ucdavis.edu>


Dear Nils,

I attach two plots with the latest data:  U=8, 12, and 15 are now added
to the U=10 results.  You already have U=8 from our old paper.  I just
ran it again to get smaller error bars.  The only difference between the
plot are the ranges of the x and y axes.  I also attach the data files.

Do you and Elena use xmgrace?  I can send the agr files also, if you
like.  (I like xmgrace since the data comes along with the graphics file
automatically.)

I was at first little surprised with how small the Trotter errors are
at U=15 compared to U=10.  The usual argument is that the errors go as
epsilon = t*U*dtau^2.  For the two U=10 runs this parameter is
epsilon=0.156, 0.069 while for the U=15 runs epsilon=0.058, 0.038.  So I
think it's just that the dtau values were chosen more conservatively for
U=15.

When do you think you might start putting this all together in a paper?
I have a tiny psychological dilemma:  My colleague Thereza Paiva has
been doing most of the runs for our current project on the 3D Hubbard model in a trap.  So I feel a little funny letting her do all that work
while my effort goes towards a totally different project.   If a paper
with you and Elena is a month or more away, we could continue to
exchange numbers and discussions and wait to see how other details
settle out.

However that all goes, I certainly am looking forward to understanding
the physics of this better.

Best Regards,
Richard



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/

nupndnU15dt0.0500avg.dat

   0.10000  10.00000   0.16120   0.00002   0.00006
   0.20000   5.00000   0.09613   0.00005   0.00010
   0.30000   3.33333   0.05692   0.00007   0.00007
   0.40000   2.50000   0.03538   0.00002   0.00006
   0.50000   2.00000   0.02380   0.00003   0.00006
   0.60000   1.66667   0.01754   0.00002   0.00005
   0.70000   1.42857   0.01417   0.00001   0.00004
   0.80000   1.25000   0.01238   0.00002   0.00003
   1.00000   1.00000   0.01086   0.00003   0.00004
   1.20000   0.83333   0.01059   0.00000   0.00004
   1.60000   0.62500   0.01053   0.00005   0.00015
   2.00000   0.50000   0.01148   0.00013   0.00014
   2.40000   0.41667   0.01204   0.00025   0.00014
   2.80000   0.35714   0.01276   0.00011   0.00015
   3.20000   0.31250   0.01336   0.00005   0.00014
   4.00000   0.25000   0.01413   0.00008   0.00014
   4.80000   0.20833   0.01486   0.00013   0.00017
   5.60000   0.17857   0.01564   0.00013   0.00015
   6.40000   0.15625   0.01630   0.00007   0.00019
   7.20000   0.13889   0.01649   0.00007   0.00015
   8.00000   0.12500   0.01690   0.00016   0.00015
   9.60000   0.10417   0.01743   0.00009   0.00011


nupndnU15dt0.0500avg.dat

   0.10000  10.00000   0.16120   0.00002   0.00006
   0.20000   5.00000   0.09613   0.00005   0.00010
   0.30000   3.33333   0.05692   0.00007   0.00007
   0.40000   2.50000   0.03538   0.00002   0.00006
   0.50000   2.00000   0.02380   0.00003   0.00006
   0.60000   1.66667   0.01754   0.00002   0.00005
   0.70000   1.42857   0.01417   0.00001   0.00004
   0.80000   1.25000   0.01238   0.00002   0.00003
   1.00000   1.00000   0.01086   0.00003   0.00004
   1.20000   0.83333   0.01059   0.00000   0.00004
   1.60000   0.62500   0.01053   0.00005   0.00015
   2.00000   0.50000   0.01148   0.00013   0.00014
   2.40000   0.41667   0.01204   0.00025   0.00014
   2.80000   0.35714   0.01276   0.00011   0.00015
   3.20000   0.31250   0.01336   0.00005   0.00014
   4.00000   0.25000   0.01413   0.00008   0.00014
   4.80000   0.20833   0.01486   0.00013   0.00017
   5.60000   0.17857   0.01564   0.00013   0.00015
   6.40000   0.15625   0.01630   0.00007   0.00019
   7.20000   0.13889   0.01649   0.00007   0.00015
   8.00000   0.12500   0.01690   0.00016   0.00015
   9.60000   0.10417   0.01743   0.00009   0.00011


nupndnU8dt0.1250avg.dat

   0.25000   4.00000   0.13968   0.00002   0.00009
   0.50000   2.00000   0.08396   0.00008   0.00011
   0.75000   1.33333   0.06099   0.00005   0.00010
   1.00000   1.00000   0.05113   0.00002   0.00011
   1.25000   0.80000   0.04654   0.00002   0.00010
   1.50000   0.66667   0.04434   0.00004   0.00012
   1.75000   0.57143   0.04333   0.00003   0.00011
   2.00000   0.50000   0.04292   0.00005   0.00009
   2.50000   0.40000   0.04295   0.00010   0.00015
   3.00000   0.33333   0.04331   0.00006   0.00011
   4.00000   0.25000   0.04540   0.00005   0.00010
   5.00000   0.20000   0.04667   0.00005   0.00012
   6.00000   0.16667   0.04723   0.00003   0.00011
   7.00000   0.14286   0.04758   0.00003   0.00015
   8.00000   0.12500   0.04763   0.00004   0.00010
  10.00000   0.10000   0.04778   0.00008   0.00008
  12.00000   0.08333   0.04781   0.00006   0.00005
  14.00000   0.07143   0.04777   0.00005   0.00006
  16.00000   0.06250   0.04775   0.00005   0.00007


nupndnU8dt0.0833avg.dat

   0.16666   6.00024   0.17157   0.00001   0.00006
   0.33332   3.00012   0.11695   0.00002   0.00010
   0.49998   2.00008   0.08550   0.00006   0.00009
   0.66664   1.50006   0.06832   0.00007   0.00008
   0.83330   1.20005   0.05869   0.00001   0.00007
   0.99996   1.00004   0.05309   0.00008   0.00009
   1.16662   0.85718   0.04977   0.00002   0.00010
   1.33328   0.75003   0.04778   0.00007   0.00009
   1.66660   0.60002   0.04572   0.00007   0.00009
   1.99992   0.50002   0.04522   0.00004   0.00008
   2.66656   0.37502   0.04574   0.00004   0.00006
   3.33320   0.30001   0.04672   0.00004   0.00008
   3.99984   0.25001   0.04823   0.00002   0.00016
   4.66648   0.21429   0.04928   0.00003   0.00012
   5.33312   0.18751   0.04981   0.00017   0.00021
   6.66640   0.15001   0.05071   0.00003   0.00008
   7.99968   0.12501   0.05101   0.00002   0.00006
   9.33296   0.10715   0.05105   0.00005   0.00007
  10.66624   0.09375   0.05112   0.00003   0.00006
  13.33280   0.07500   0.05105   0.00005   0.00007


nupndnU12dt0.0833avg.dat

   0.16660   6.00240   0.13691   0.00002   0.00009
   0.33320   3.00120   0.07125   0.00004   0.00011
   0.49980   2.00080   0.04114   0.00005   0.00006
   0.66640   1.50060   0.02776   0.00005   0.00008
   0.83300   1.20048   0.02176   0.00005   0.00005
   0.99960   1.00040   0.01896   0.00003   0.00005
   1.16620   0.85749   0.01775   0.00003   0.00008
   1.33280   0.75030   0.01736   0.00003   0.00006
   1.66600   0.60024   0.01740   0.00003   0.00008
   1.99920   0.50020   0.01749   0.00008   0.00012
   2.66560   0.37515   0.01948   0.00006   0.00015
   3.33200   0.30012   0.02058   0.00008   0.00016
   3.99840   0.25010   0.02167   0.00012   0.00019
   4.66480   0.21437   0.02269   0.00011   0.00016
   5.33120   0.18758   0.02329   0.00012   0.00014
   6.66400   0.15006   0.02428   0.00014   0.00016
   7.99680   0.12505   0.02471   0.00004   0.00010
   9.32960   0.10719   0.02482   0.00007   0.00012
  10.66240   0.09379   0.02497   0.00002   0.00006