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HPhi Developers committed Mar 7, 2024
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4 changes: 4 additions & 0 deletions manual/v3.5.2/en/html/.buildinfo
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# Sphinx build info version 1
# This file hashes the configuration used when building these files. When it is not found, a full rebuild will be done.
config: 783f03ac2d303b081fba6b5a7e6fe0a8
tags: 645f666f9bcd5a90fca523b33c5a78b7
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model = "Hubbard"
lattice = "wannier90"
a0w = 8
a0l = 0
a0h = 8
a1w = 0
a1l = 1
a1h = 0
a2w = 1
a2l = 0
a2h = 0
method = "TPQ"
nelec = 8
exct = 1
cutoff_t = 0.5
cutoff_u = 1.0
cutoff_j = 0.02
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model = "Hubbard"
lattice = "wannier90"
a0w = 2
a0l = 0
a0h = 2
a1w = 0
a1l = 2
a1h = 2
a2w = 1
a2l = 0
a2h = 0
method = "CG"
2Sz = 0
nelec = 4
exct = 1
cutoff_t = 0.2
cutoff_u = 0.4
cutoff_j = 0.1
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&BANDS
prefix = 'sr2cuo3'
lsym = .false.
/
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&PARAM_CHIQW
Num_freq_grid = 1
!Ecut_for_eps =
flg_cRPA = 1
/
&PARAM_WANNIER
N_wannier = 1
Lower_energy_window = 8
Upper_energy_window = 13
N_initial_guess = 1
/
dx2 0.2 0.500000 0.000000 0.50000 0.0 0.0 1.0 0.0 1.0 0.0 1.0 0.0 0.0
&PARAM_INTERPOLATION
N_sym_points = 10
!dense = 20, 24, 28
/
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iy_vis_min = -1,
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iz_vis_min = -1,
iz_vis_max = 2
/
&PARAM_CALC_INT
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ix_intJ_min = -1
ix_intJ_max = 1
iy_intJ_min = -1
iy_intJ_max = 1
iz_intJ_min = -1
iz_intJ_max = 1
/
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&CONTROL
calculation = 'nscf'
pseudo_dir = '../pseudo'
wf_collect = .true.
prefix = 'sr2cuo3'
/
&SYSTEM
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nat = 6
ntyp = 3
ecutwfc = 30.000000
ecutrho = 240.000000
occupations = 'tetrahedra_opt'
nbnd = 35
/
&ELECTRONS
/
CELL_PARAMETERS angstrom
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1.749305 -1.955690 6.351200
1.749305 1.955690 -6.351200
ATOMIC_SPECIES
Sr 87.620000 Sr_ONCV_PBE-1.0.upf
Cu 63.546000 Cu_ONCV_PBE-1.0.upf
O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
Sr 0.851940 0.351940 0.500000
Sr 0.148060 0.648060 0.500000
Cu 0.500000 0.000000 0.500000
O 0.654110 0.154110 0.500000
O 0.345890 0.845890 0.500000
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4 4 4 0 0 0
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&CONTROL
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/
&SYSTEM
ibrav = 0
nat = 6
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ecutrho = 240.000000
nbnd = 35
/
&ELECTRONS
/
CELL_PARAMETERS angstrom
-1.749305 1.955690 6.351200
1.749305 -1.955690 6.351200
1.749305 1.955690 -6.351200
ATOMIC_SPECIES
Sr 87.620000 Sr_ONCV_PBE-1.0.upf
Cu 63.546000 Cu_ONCV_PBE-1.0.upf
O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
Sr 0.851940 0.351940 0.500000
Sr 0.148060 0.648060 0.500000
Cu 0.500000 0.000000 0.500000
O 0.654110 0.154110 0.500000
O 0.345890 0.845890 0.500000
O 0.000000 0.000000 0.000000
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&CONTROL
calculation = 'scf'
pseudo_dir = '../pseudo'
prefix = 'sr2cuo3'
/
&SYSTEM
ibrav = 0
nat = 6
ntyp = 3
ecutwfc = 30.000000
ecutrho = 240.000000
occupations = 'tetrahedra_opt'
/
&ELECTRONS
mixing_beta = 0.3
/
CELL_PARAMETERS angstrom
-1.749305 1.955690 6.351200
1.749305 -1.955690 6.351200
1.749305 1.955690 -6.351200
ATOMIC_SPECIES
Sr 87.620000 Sr_ONCV_PBE-1.0.upf
Cu 63.546000 Cu_ONCV_PBE-1.0.upf
O 15.999400 O_ONCV_PBE-1.0.upf
ATOMIC_POSITIONS crystal
Sr 0.851940 0.351940 0.500000
Sr 0.148060 0.648060 0.500000
Cu 0.500000 0.000000 0.500000
O 0.654110 0.154110 0.500000
O 0.345890 0.845890 0.500000
O 0.000000 0.000000 0.000000
K_POINTS automatic
4 4 4 0 0 0
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16 changes: 16 additions & 0 deletions manual/v3.5.2/en/html/_sources/acknowledgement_en.rst.txt
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***************
Acknowledgement
***************

We would like to express our sincere gratitude to Prof. Hidetoshi Nishimori and Mr. Daisuke Tahara.
Implementation of the Lanczos algorithm in :math:`{\mathcal H}\Phi` written in C is based on the
pioneering diagonalization package TITPACK written in Fortran by Prof. Nishimori.
For developing the user interface of :math:`{\mathcal H}\Phi`, we followed the design concept of
the user interface in the program for variational Monte Carlo developed by Mr. Tahara.
A part of the user interface in :math:`{\mathcal H}\Phi` is based on his original codes.
We would also like to express our thanks for the support of the \"*Project for advancement of software usability in materials science*\" of The Institute for Solid State Physics, The University of Tokyo, for the development of :math:`{\mathcal H}\Phi` ver. 0.1 - ver. 2.0.4

Dr. Yuichi Motoyama and Dr. Yasuyuki Kato found and reported bugs.
We acknowledge their kindness and carefulness.

We thank Prof. Takeo Hoshi and Prof. Tomohiro Sogabe for the fruitful discussions on the shifted Krylov method and the development of the :math:`K\omega` library.
26 changes: 26 additions & 0 deletions manual/v3.5.2/en/html/_sources/algorithm/Bogoliubov_en.rst.txt
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.. highlight:: none

.. _Sec:sec_bogoliubov_rep:

Bogoliubov representation
=========================


In the spin system,
the spin indices in the input files of ``transfer``, ``InterAll``,
and correlation functions are specified as those of the Bogoliubov representation.
The spin operators are written by using creation\/annihilation operators:

.. math::
S_{i z} &= \sum_{\sigma = -S}^{S} \sigma c_{i \sigma}^\dagger c_{i \sigma}
\\
S_{i}^+ &= \sum_{\sigma = -S}^{S-1}
\sqrt{S(S+1) - \sigma(\sigma+1)}
c_{i \sigma+1}^\dagger c_{i \sigma}
\\
S_{i}^- &= \sum_{\sigma = -S}^{S-1}
\sqrt{S(S+1) - \sigma(\sigma+1)}
c_{i \sigma}^\dagger c_{i \sigma+1}
In HPhi, the index of the highest-:math:`\sigma` state is 0.
33 changes: 33 additions & 0 deletions manual/v3.5.2/en/html/_sources/algorithm/DynamicalGreen_en.rst.txt
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.. highlight:: none

Dynamical Green’s function
--------------------------

Using :math:`{\mathcal H}\Phi`, we can calculate a dynamical Green’s
function

.. math:: I(z) = \langle \Phi ' | \frac{1}{ {\mathcal H}- z\hat{I} } | \Phi '\rangle,

where :math:`|\Phi ' \rangle = \hat{O} | \Phi _0 \rangle` is an
excited state and :math:`\hat{O}` is an excitation operator defined as a
single excitation operator

.. math:: \sum_{i, \sigma_1} A_{i \sigma_1} c_{i \sigma_1} (c_{i\sigma_1}^{\dagger})

or a pair excitation operator

.. math:: \sum_{i, j, \sigma_1, \sigma_2} A_{i \sigma_1 j \sigma_2} c_{i \sigma_1}c_{j \sigma_2}^{\dagger} (c_{i\sigma_1}^{\dagger}c_{j\sigma_2}).

For example, the dynamical spin susceptibilities can be calculated by
defining :math:`\hat{O}` as

.. math:: \hat{O} = \hat{S}({\bf k}) = \sum_{j}\hat{S}_j^z e^{i {\bf k} \cdot \bf {r}_j} = \sum_{j}\frac{1}{2} (c_{j\uparrow}^{\dagger}c_{j\uparrow}-c_{j\downarrow}^{\dagger}c_{j\downarrow})e^{i {\bf k} \cdot \bf {r}_j}.

There are two modes implemented in :math:`{\cal H}\Phi`. One is the
continued fraction expansion method by using Lanczos method
 [#]_ and the other is the shifted Krylov
method [#]_ . See the reference
for the details of each algorithm.

.. [#] \E. Dagotto, Rev. Mod. Phys. **66**, 763-840 (1994).
.. [#] \S.Yamamoto, T. Sogabe, T. Hoshi, S.-L. Zhang, T. Fujiwara, Journal of the Physical Society of Japan **77**, 114713 (2008).
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.. highlight:: none

Full Diagonalization method
===========================

Overview
--------

We generate the matrix of :math:`\hat{\mathcal H }` by using the real space configuration
:math:`| \psi_j \rangle`\(:math:`j=1\cdots d_{\rm H}`, where :math:`d_{\rm H}` is the dimension of the Hilbert space):
:math:`{\mathcal H }_{ij}= \langle \psi_i | \hat {\mathcal H } | \psi_j \rangle`.
By diagonalizing this matrix,
we can obtain all the eigenvalues :math:`E_{i}` and eigenvectors :math:`|\Phi_i\rangle` (:math:`i=1 \cdots d_{\rm H}`).
In the diagonalization, we use a LAPACK routine, such as ``dsyev`` or ``zheev``.
We also calculate and output
the expectation values :math:`A_i \equiv \langle \Phi_i | {\hat A} | \Phi_i\rangle`.
These values are used for the finite-temperature calculations.

Finite-temperature calculations
-------------------------------

From
:math:`A_i \equiv \langle \Phi_i | {\hat A} | \Phi_i\rangle`,
we calculate the finite-temperature properties by using the relation

.. math::
\langle {\hat A}\rangle=\frac{\sum_{i=1}^N A_i {\rm e}^{-\beta E_i}}{\sum_{i=1}^N{\rm e}^{-\beta E_i}}.
The calculation should be performed by using the own postscripts.
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