File format¶
Geometry¶
The file name in the Tutorial is geometry.dat.
When we use Standard mode of mVMC/\({\mathcal H}\Phi\),
the information of the cell and geometry is generated automatically.
1.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 (1)
0.000000000000000e+00 1.000000000000000e+00 0.000000000000000e+00 (1)
0.000000000000000e+00 0.000000000000000e+00 1.000000000000000e+00 (1)
0.000000000000000e+00 0.000000000000000e+00 0.000000000000000e+00 (2)
2 2 0 (3)
-2 2 0 (3)
0 0 1 (3)
0 0 0 0 (4)
-1 1 0 0 (4)
0 1 0 0 (4)
1 1 0 0 (4)
-1 2 0 0 (4)
0 2 0 0 (4)
1 2 0 0 (4)
0 3 0 0 (4)
4 20 (5)
G 0 0 0 (6)
X 0.5 0 0 (6)
M 0.5 0.5 0 (6)
G 0 0 0 (6)
16 16 1 (7)
- The unit lattice vectors. Arbitrary unit (Generated by Standard mode).
- The phase for the one-body term across boundaries of the simulation cell (degree unit, Generated by Standard mode).
- Three integer vector specifying the shape of the simulation cell.
They are the same as the input parameters
a0W,a0L,a0H,a1W… in Standard mode (Generated by standard mode). - The index of the lattice vector and the orbital each site (Generated by standard mode).
- The number of k node (high-symmetry point) and the number of k along high symmetry line.
- Fractional coordinate of k nodes.
- The k grid to plot the isosurface of the momentum distribution function.
One- and Two-body correlation function in the site representation¶
Specify the index of correlation function to be computed¶
Specify the index of correlation functions
computed with mVMC/\({\mathcal H}\Phi\).
When we use the standard mode, this file is generated automatically.
The general description is written in the manuals for mVMC/\({\mathcal H}\Phi\).
The file names in the Tutorial are greenone.def (one body) and greentwo.def (two body).
For calculating correlation functions in Supported quantities, indices must be specified as follows:
\(\langle {\hat c}_{{\bf k}\alpha\uparrow}^{\dagger} {\hat c}_{{\bf k}\beta\uparrow}\rangle\)
\(\langle {\hat c}_{{\bf 0}\alpha\uparrow}^{\dagger} {\hat c}_{{\bf R}\beta\uparrow}\rangle\) with \({\bf R}\) ranging on the all unit cell, and \((\alpha, \beta)\) ranging on the all orbitals in the unit cell.
\(\langle {\hat c}_{{\bf k}\alpha\downarrow}^{\dagger} {\hat c}_{{\bf k}\beta\downarrow}\rangle\)
\(\langle {\hat c}_{{\bf 0}\alpha\downarrow}^{\dagger} {\hat c}_{{\bf R}\beta\downarrow}\rangle\) with \({\bf R}\) ranging on the all unit cell, and \((\alpha, \beta)\) ranging on the all orbitals in the unit cell.
\(\langle {\hat \rho}_{{\bf k}\alpha} {\hat \rho}_{{\bf k}\beta}\rangle\) and \(\langle {\hat S}_{{\bf k}\alpha}^{z} {\hat S}_{{\bf k}\beta}^{z} \rangle\)
\(\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha\sigma} {\hat c}_{{\bf R}\beta \sigma'}^{\dagger} {\hat c}_{{\bf R}\beta \sigma'}\rangle\) with \({\bf R}\) ranging on the all unit cell, \((\alpha, \beta)\) ranging on the all orbitals in the unit cell, and \((\sigma, \sigma')\) ranging from \(\uparrow\) to \(\downarrow\).
\(\langle {\hat S}_{{\bf k}\alpha}^{+} {\hat S}_{{\bf k}\beta}^{-} \rangle\) and \(\langle {\hat {\bf S}}_{{\bf k}\alpha} \cdot {\hat {\bf S}}_{{\bf k}\beta} \rangle\)
For \({\mathcal H}\Phi\), \(\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha-\sigma} {\hat c}_{{\bf R}\beta -\sigma}^{\dagger} {\hat c}_{{\bf R}\beta \sigma}\rangle\) with \({\bf R}\) ranging on the all unit cell, \((\alpha, \beta)\) ranging on the all orbitals in the unit cell, and \(\sigma\) ranging from \(\uparrow\) to \(\downarrow\). For mVMC, \(\langle {\hat c}_{{\bf 0}\alpha\sigma}^{\dagger} {\hat c}_{{\bf R}\beta \sigma} {\hat c}_{{\bf R}\beta -\sigma}^{\dagger} {\hat c}_{{\bf 0}\alpha-\sigma}\rangle\) with \({\bf R}\) ranging on the all unit cell, \((\alpha, \beta)\) ranging on the all orbitals in the unit cell, and \(\sigma\) ranging from \(\uparrow\) to \(\downarrow\). In the both cases, please care the order of operators.
In the default settings of Standard mode (outputmode="corr"),
the above indices are specified automatically.
Therefore we do not have to care it.
Results of correlation function in the site representation¶
The correlation functions having the indices specified in Specify the index of correlation function to be computed
are computed by mVMC/\({\mathcal H}\Phi\),
and written to files.
The general description of this file is written in the manuals of mVMC/\({\mathcal H}\Phi\).
File names in the Tutorial are
output/zvo_cisajs_001.dat and output/zvo_cisajscktalt_001.dat (mVMC), or
output/zvo_cisajs.dat and output/zvo_cisajscktalt.dat (\({\mathcal H}\Phi\)).
The utility fourier reads these files before the calculation.
If some of the correlation functions with indices written in Specify the index of correlation function to be computed are lacking
(for example, because Standard mode was not used),
this utility assume them as 0.
Correlation functions on the k path¶
This file contains the Fourier-transformed correlation function and
generated by the utility fourier.
The file name in the Tutorial is output/zvo_corr.dat.
# k-length[1]
# Orbital 1 to Orbital 1
# UpUp[ 2, 3] (Re. Im.) DownDown[ 4, 5]
# Density[ 6, 7] SzSz[ 8, 9] S+S-[ 10, 11] S.S[ 12, 13]
0.00000E+00 0.88211E+00 -0.50000E-09 0.88211E+00 0.40000E-09 ...
0.25000E-01 0.87976E+00 -0.46625E-09 0.87976E+00 0.42882E-09 ...
0.50000E-01 0.87276E+00 -0.42841E-09 0.87276E+00 0.45201E-09 ...
: :
First, the information of the quantities at each column is written, and then the k coordinate along the path and the real- and imaginary- part of the correlation function are written.
gnuplot script¶
This file is generated by greenr2k.
This script is used for displaying the k labels in gnuplot.
The file name is kpath.gp.
set xtics ('G' 0.00000, 'X' 0.50000, 'M' 1.00000, 'G' 1.70711)
set ylabel 'Correlation function'
set grid xtics lt 1 lc 0
FermiSurfer file to display the isosurface of the momentum distribution¶
This file is generated by greenr2k.
The file name in the tutorial is output/zvo_corr_eigen0.dat.frmsf.
