calculate the condensate fraction of excitons

General discussion of the Cambridge quantum Monte Carlo code CASINO; how to install and setup; how to use it; what it does; applications.
Post Reply
braulio
Posts: 6
Joined: Wed Aug 21, 2013 11:32 am
Location: Instituto de Física de São Carlos-USP
Contact:

calculate the condensate fraction of excitons

Post by braulio »

Hello the Casino users

I am struggling to calculate the condensate fraction of excitons in an electron-hole system using DMC. My question is: This is very time consuming to calculate? I did the following run test: 58 electron, 58 holes, Nwalkers=10 and Nstep=100 the time to performe one block took two hours using 4 i7 processors 3.0 GHz . There are some way to speed up the calculations? or I am doing something wrong.
Pablo_Lopez_Rios
Posts: 53
Joined: Thu Jan 30, 2014 1:25 am

Re: calculate the condensate fraction of excitons

Post by Pablo_Lopez_Rios »

Hi Braulio,

The accumulation parameters can be tuned to reduce the cost of the run. Unfortunately due to the design of the expval.data file format the process is somewhat fiddly.

You will need to:
  • Starting from an existing expval.data file, delete the CONDENSATE FRACTION block and replace it with:
  • [code] START CONDENSATE FRACTION Accumulation carried out using DMC Number of sets 1 Number of bins 100 Number of random points to sample 20 Fraction of particle pairs to sample at random 0.0500 START SET 1 Number of particle-pair types in set 4 Particle-pair types 1 3 2 3 1 4 2 4 Weight(r),CF(r)**2,CF(r) END SET 1 END CONDENSATE FRACTION [/code] This will only accumulate the electron-hole expectation value and ignore the electron-electron and hole-hole components which are computed by default. [/*]
  • In the above I have modified the "Fraction of particle pairs" parameter. By default, the code goes over all 58^2 (=3364) electron-hole pairs, but it can go over a random sample of them instead. With the above "Fraction of particle pairs" value of 0.05, the code will sample a random 5% of the 58^2 electron-hole pairs (=168) at each step, reducing the cost of the evaluation per DMC step by a factor of 20. This will also affect the statistics of the result, of course, but overall it is advantageous to use a value << 1.0 here.
  • If you want, modify the "Number of random points" parameter. This controls the number of random electron-hole pair displacements sampled for each electron-hole pair at each step. In my opinion the default value of 20 is generally sensible.
  • If you want more or less resolution in the final plot, change the "Number of bins" from 100 to whichever value you'd like. The finer the grid, the poorer the statistics. In my opinion the default value of 100 is generally sensible.
  • If you are accumulating any other expectation values in the expval.data file, make sure you delete the data lines in all sets, as above, to start the accumulation afresh.
  • Make a copy of expval.data in case you need to start over, since expval.data is overwritten when CASINO is run.
  • Now run your calculation.
Note that I've assumed that you are accumulating the "cond_fraction" estimator, which is a non-standard estimator with clear statistical advantages near the origin, but tends to exhibit outliers in the tail (the important bit to compute the condensate fraction) and has never been used in the literature. It is also possible to accumulate the standard estimator by toggling the "onep_density_mat" and "twop_density_mat" input keywords. If you choose to plot the two-body density matrix in the plot_expval utility, it will offer to subtract the one-particle density matrix, giving the standard estimator of the condensate fraction. You may want to modify the default accumulation parameters for these expectation values as above, giving:

Code: Select all

START ONE-PARTICLE DENSITY MATRIX
Accumulation carried out using
 DMC
Number of sets
 2
Number of bins
 100
Number of random points to sample
 20
START SET 1
Number of particle types in set
 2
Particle types
 1 2
Weight(r),OBDM(r)**2,OBDM(r)
END SET 1
START SET 2
Number of particle types in set
 2
Particle types
 3 4
Weight(r),OBDM(r)**2,OBDM(r)
END SET 2
END ONE-PARTICLE DENSITY MATRIX

START TWO-PARTICLE DENSITY MATRIX
Accumulation carried out using
 DMC
Number of sets
 1
Number of bins
 100
Number of random points to sample
 20
Fraction of particle pairs to sample at random
 0.0500
START SET 1
Number of particle-pair types in set
 4
Particle-pair types
 1 3  2 3  1 4  2 4
Weight(r),TBDM(r)**2,TBDM(r)
END SET 1
END TWO-PARTICLE DENSITY MATRIX
Hope that helps!

Best,
Pablo
Hey there! I am using CASINO.
Mike Towler
Posts: 239
Joined: Thu May 30, 2013 11:03 pm
Location: Florence
Contact:

Re: calculate the condensate fraction of excitons

Post by Mike Towler »

Good answer! I'll stick it in the manual.. :D

M.
braulio
Posts: 6
Joined: Wed Aug 21, 2013 11:32 am
Location: Instituto de Física de São Carlos-USP
Contact:

Re: calculate the condensate fraction of excitons

Post by braulio »

Thanks for the tip.
Post Reply