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| README | ||
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README
This example shows how to generate a model Hamiltonian in Wannier functions basis.
Detailes of the method are described in:
[1] Dm. Korotin, A. V. Kozhevnikov, S. L. Skornyakov, I. Leonov, N. Binggeli, V. I. Anisimov, and G. Trimarchi, The European Physical Journal B 65, 91-98 (2008).
Generation of a model Hamiltonian consists of three steps:
1. Typical scf calculation. We need converged charge density.
2. Nscf calculation on a regular and dense k-points grid (at least 12x12x12 for reasonable Hamiltonian). Please set
nosym=.true.
noinv=.true.
integration='smearing'
degauss=0.01
wf_collect=.true. (if you run parallel job)
in &control namelist
From nscf calculation we need eigenvalues and eigenvectors of full Hamiltonian on every k-point and the Fermi energy (for Wannier functions occupation calculation).
3. Before you will start the model Hamiltonian generation you should know a symmetry of trial atomic orbitals that will be used for projection. And you should know numbers of bands (or energy interval) that you are going to reproduce with the model Hamiltonian. In the current example of NiO we will generate
8 Wannier functions (5 with Ni-d orbitals symmetry and 3 with O-p orbitals symmetry).
The code wannier_ham.x will produce file 'hamilt' with the Hamiltonian for every k-point
Structure of the input data:
===============================================================================
&INPUTPP
...
/
WANNIER_AC
Wannier# 1 2 9
atom 1
d 2
Wannier# 2 2 9
atom 1
d 3
Wannier# 3 2 9
atom 1
d 5
...
========================================================================
NAMELIST: &INPUTPP
+--------------------------------------------------------------------
Variable: prefix
Type: CHARACTER
Default: ' '
Description: as usual
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variable: outdir
Type: CHARACTER
Default: ' '
Description: as usual
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variable: nwan
Type: INTEGER
Default: ' '
Description: Number of Wannier functions
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variable: use_energy_int
Type: LOGICAL
Default: '.FALSE.'
Description: If .true. bands will be defined not by numbers, but by
energy range (in eV)!
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variable: plot_bands
Type: LOGICAL
Default: '.FALSE.'
Description: If .true. bands structures of original and model hamiltonian
will be plotted for comparison
+--------------------------------------------------------------------
========================================================================
CARD: WANNIER_AC
Definition of trial atomic functions and bands for Wannier generation
/////////////////////////////////////////
// Syntax: //
/////////////////////////////////////////
Wannier# 1 bands_from bands_to
atom iatom
l m
Wannier# 2 bands_from bands_to
atom iatom
l m
...
/////////////////////////////////////////
DESCRIPTION OF ITEMS:
+--------------------------------------------------------------------
Variables: bands_from, bands_to
Type: REAL or INTEGER
Description: Defines Block functions subspace for projection
procedure. If use_energy_interval=.true. these are
energy values in eV. Otherwise these are bands numbers.
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variables: iatom
Type: INTEGER
Description: Number of site on that Wannier function centered
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variables: l
Type: CHARACTER
Description: Angular channel for trial wavefunction. 's', 'p' or 'd'
+--------------------------------------------------------------------
+--------------------------------------------------------------------
Variables: m
Type: INTEGER
Description: Magnetic quantum number of trial orbital (from 1 to 5)
for d-orbitals
+--------------------------------------------------------------------
===END OF CARD==========================================================
Format of 'hamilt' file:
===============================================================================
num_of_k-points dimention_of_Hamiltonian
k-point_weight
Real(H(1,1)) Imag(H(1,1))
Real(H(2,1)) Imag(H(2,1))
....
k-point_weight
Real(H(1,1)) Imag(H(1,1))
Real(H(2,1)) Imag(H(2,1))
....