CASINO manual - Theory of Condensed Matter

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