CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
CASINO manual - Theory of Condensed Matter
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total weight must always be included alongside the data so that further accumulation steps<br />
can be carried out. The correct way to perform additional accumulation is to set<br />
new tot. weight = old tot. weight + new weight (8)<br />
new tot. data =<br />
old tot. weight × old tot. data + new weight × new data<br />
.<br />
new tot. weight<br />
(9)<br />
The ‘new total weight’ and ‘new total data’ should be written out to expval.data.<br />
(c) Sets <strong>of</strong> reciprocal space vectors (‘G-vectors’) are specified at the start <strong>of</strong> the file and are<br />
then referenced by the different sets in the file, because expectation values for different<br />
operators are <strong>of</strong>ten accumulated using the same set <strong>of</strong> G-vectors.<br />
(d) Each <strong>of</strong> the subsequent data sets is optional. If a data set is present when this file is read<br />
as input, but casino is not accumulating further data for this set, then the set must be<br />
copied verbatim on output.<br />
(e) It is permitted to have, for example, the VMC-accumulated charge density present in this<br />
file, to be used for the MPC interaction in a DMC calculation whilst accumulating, for<br />
example, the pair-correlation function.<br />
2. Notes on the ‘density’ data set:<br />
(a) There should be one set <strong>of</strong> data present for each type <strong>of</strong> particle (electron, hole).<br />
(b) The normalization <strong>of</strong> the data for a given particle type is such that the G = 0 component<br />
is equal to the total number <strong>of</strong> particles <strong>of</strong> that type in the primitive cell. This is naturally<br />
the result if the data is accumulated during the simulation, then divided by the total weight<br />
(that is, the number <strong>of</strong> accumulation steps) then divided by the number <strong>of</strong> primitive cells<br />
in the simulation cell.<br />
(c) The QMC charge density may be used in the MPC interaction, if desired.<br />
3. Notes on the ‘spin density’ data set:<br />
(a) The format <strong>of</strong> this section is the same as that <strong>of</strong> the ‘density’ section, except that there are<br />
two sets <strong>of</strong> data for each particle type, to allow for up and down spins.<br />
4. Notes on the ‘spin-density matrix’ data set:<br />
(a) These data can be obtained when using the noncollinear-spin mode <strong>of</strong> casino. There are<br />
separate 2 × 2 spin-density matrices for each particle type.<br />
(b) Due to the way in which noncollinear spins are implemented in casino, it would be possible<br />
in principle to have a separate set <strong>of</strong> data for up-like electrons, down-like electrons, up-like<br />
holes and so on. In practice this does not make sense, and only one type <strong>of</strong> electron and<br />
one type <strong>of</strong> hole should be used.<br />
(c) The plot expval utility will give you the option to plot either the spin-density matrix<br />
itself or the magnetization density, which is derived from the spin-density matrix.<br />
5. Notes on the ‘reciprocal-space pair-correlation function’ data set:<br />
(a) This data set contains the Fourier coefficients <strong>of</strong> the pair-correlation function, accumulated<br />
with the position <strong>of</strong> one particle being fixed.<br />
(b) Apart from information on the type and location <strong>of</strong> the fixed particle, the format <strong>of</strong> this<br />
data set is identical to the ‘spin density’ set.<br />
6. Notes on the ‘spherical pair-correlation function’ data set:<br />
(a) This set contains a real-space representation <strong>of</strong> the pair-correlation function, obtained by<br />
binning particle separations.<br />
(b) There are two slightly different ways in which spherical PCFs may be accumulated. For<br />
homogeneous and finite systems, we accumulate the spherical PCF based on the relative<br />
distances <strong>of</strong> all pairs <strong>of</strong> particles. For inhomogeneous and periodic systems, we must accumulate<br />
the spherical PCF as the distance <strong>of</strong> all other particles from one fixed particle.<br />
(c) The format <strong>of</strong> this set is flexible enough to allow for both methods. Two examples are<br />
given above to show the two possible scenarios.<br />
(d) When the data is for fixed-particle accumulation, the first <strong>of</strong> the two particle types appearing<br />
on the ‘Types <strong>of</strong> particles in pair’ line must be that <strong>of</strong> the fixed particle.<br />
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