## 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,

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!