## Problem obtaining static structure factor

General discussion of the Cambridge quantum Monte Carlo code CASINO; how to install and setup; how to use it; what it does; applications.
ankush
Posts: 3
Joined: Fri Mar 27, 2020 6:29 pm

### Problem obtaining static structure factor

Respected CASINO developers,

I am not able to obtain correct static structure factor in finite polarization calculations of one- dimensional Harmonic wire system. There is some problem with normalization along y-axis. For the same calculation, I am getting a correct pair correlation function and correct ground state energy.

Regards,
Ankush
Neil Drummond
Posts: 95
Joined: Fri May 31, 2013 10:42 am
Location: Lancaster
Contact:

### Re: Problem obtaining static structure factor

Dear Ankush,

Thanks for the question. I was wondering if you could clarify what the problem is? I've just tried running a harmonic wire VMC calculation and I can't see any problem with the static structure factor. I calculated the structure factor by setting structure_factor to T in the input file, then plotting it using plot_expval.

Best wishes,

Neil.
ankush
Posts: 3
Joined: Fri Mar 27, 2020 6:29 pm

### Re: Problem obtaining static structure factor

Respected Sir,

Thanks for the quick reply!

The problem is that when I run the VMC calculation for finitely spin-polarized harmonic wire (say for zero polarization). In that case, the height of the peak of S↑↑ is not matching with already published results. For large values of k, it saturates to a value of 0.5 which must be 1. Specifically for the zero polarization case, if we multiply the y axis values with 2, we get correct results. Then what could be the justification of multiplying y-axis values with 2? Also, multiplying by 2 does not work in other non-zero polarizations say 0.25.

Regards,
Ankush
Neil Drummond
Posts: 95
Joined: Fri May 31, 2013 10:42 am
Location: Lancaster
Contact:

### Re: Problem obtaining static structure factor

Dear Ankush,

The structure factor plotted by plot_expval is normalised such that the total structure factor S(k) -> 1 as k->oo, where S(k) = sum_a sum_b S_ab(k), where a and b denote spins.

Different normalisation conventions are used in the literature (differing by factors of density N/Omega and cell volume Omega). Somewhat confusingly, the discussion of the "structure factor" and the "spherical structure factor" in the CASINO manual is an example of this!

Please adjust the normalisation as you wish by scaling the data.

Best wishes,

Neil.