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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
@@ -21,10 +21,10 @@ | |
""" | ||
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||
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||
__version__ = "0.8.12" | ||
__version__ = "0.8.13" | ||
__doclink__ = "rad-tools.org" | ||
__git_hash__ = "c59a9b2bb615c6239aeaaa4b0b73c768f2355eb9" | ||
__release_date__ = "23 November 2023" | ||
__git_hash__ = "058e6bbaeebaae0f63199f98eb38be8f9a134743" | ||
__release_date__ = "4 March 2024" | ||
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from . import ( | ||
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
@@ -83,7 +83,7 @@ def niggli( | |
A & B & C \\ | ||
\xi/2 & \eta/2 & \zeta/2 | ||
\end{pmatrix} | ||
If return_cell == True, then return Niggli cell: (a, b, c, alpha, beta, gamma). | ||
Raises | ||
|
@@ -108,7 +108,7 @@ def niggli( | |
Examples | ||
-------- | ||
Example from [1]_ | ||
(parameters are reproducing :math:`A=9`, :math:`B=27`, :math:`C=4`, | ||
(parameters are reproducing :math:`A=9`, :math:`B=27`, :math:`C=4`, | ||
:math:`\xi` = -5, :math:`\eta` = -4, :math:`\zeta = -22`): | ||
.. doctest:: | ||
|
@@ -127,7 +127,7 @@ def niggli( | |
>>> print(f"{alpha:.2f} {beta:.2f} {gamma:.2f}") | ||
103.92 109.47 134.88 | ||
>>> niggli_matrix_form = rad.niggli(a, b, c, alpha, beta, gamma, verbose=True) | ||
A B C xi eta zeta | ||
A B C xi eta zeta | ||
start: 9.00000 27.00000 4.00000 -5.00000 -4.00000 -22.00000 | ||
2 appl. to 9.00000 27.00000 4.00000 -5.00000 -4.00000 -22.00000 | ||
1 appl. to 9.00000 4.00000 27.00000 -5.00000 -22.00000 -4.00000 | ||
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
@@ -17,10 +17,10 @@ | |
# along with this program. If not, see <https://www.gnu.org/licenses/>. | ||
|
||
r""" | ||
The module provides input-output routines. | ||
The module provides input-output routines. | ||
It does not mean to absorb all interfaces to the external data formats, | ||
but designed to be the place for the constructor of the internal | ||
data structures from the input data of the external programs, | ||
but designed to be the place for the constructor of the internal | ||
data structures from the input data of the external programs, | ||
as well as from the internal-specified formats. | ||
""" | ||
|
||
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# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
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@@ -1,5 +1,5 @@ | ||
# RAD-tools - program for spin Hamiltonian and magnons. | ||
# Copyright (C) 2022-2023 Andrey Rybakov | ||
# Copyright (C) 2022-2024 Andrey Rybakov | ||
# | ||
# e-mail: [email protected], web: adrybakov.com | ||
# | ||
|
@@ -34,21 +34,21 @@ def solve_via_colpa(D): | |
.. math:: | ||
\hat{H} = \sum_{r^{\prime}, r = 1}^m | ||
\hat{H} = \sum_{r^{\prime}, r = 1}^m | ||
\hat{\alpha}_{r^{\prime}}^{\dagger}\boldsymbol{\Delta}_1^{r^{\prime}r}\hat{\alpha}_r + | ||
\hat{\alpha}_{r^{\prime}}^{\dagger}\boldsymbol{\Delta}_2^{r^{\prime}r}\hat{\alpha}_{m+r}^{\dagger} + | ||
\hat{\alpha}_{m+r^{\prime}}^{\dagger}\boldsymbol{\Delta}_3^{r^{\prime}r}\hat{\alpha}_r + | ||
\hat{\alpha}_{r^{\prime}}^{\dagger}\boldsymbol{\Delta}_2^{r^{\prime}r}\hat{\alpha}_{m+r}^{\dagger} + | ||
\hat{\alpha}_{m+r^{\prime}}^{\dagger}\boldsymbol{\Delta}_3^{r^{\prime}r}\hat{\alpha}_r + | ||
\hat{\alpha}_{m+r^{\prime}}^{\dagger}\boldsymbol{\Delta}_4^{r^{\prime}r}\hat{\alpha}_{m+r}^{\dagger} | ||
In a matrix form the Hamiltonian is: | ||
.. math:: | ||
\hat{H} = \boldsymbol{\hat{a}}^{\dagger} \boldsymbol{D} \boldsymbol{\hat{a}} | ||
where | ||
.. math:: | ||
.. math:: | ||
\boldsymbol{\hat{a}} = | ||
\begin{pmatrix} | ||
|
@@ -86,15 +86,15 @@ def solve_via_colpa(D): | |
Last N eigenvalues are sorted in ascending order. | ||
In the case of diagonalization of the magnon Hamiltonian | ||
first N eigenvalues are the same as last N eigenvalues, but | ||
in reversed order. It is an array of the diagonal elements of the | ||
in reversed order. It is an array of the diagonal elements of the | ||
diagonal matrix :math:`\boldsymbol{E}` from the diagonalized Hamiltonian. | ||
G : (2N, 2N) :numpy:`ndarray` | ||
Transformation matrix, which change the basis from the original set of bosonic | ||
operators :math:`\boldsymbol{\hat{a}}` to the set of | ||
Transformation matrix, which change the basis from the original set of bosonic | ||
operators :math:`\boldsymbol{\hat{a}}` to the set of | ||
new bosonic operators :math:`\boldsymbol{\hat{c}}` which diagonalize | ||
the Hamiltonian: | ||
.. math:: | ||
\boldsymbol{\hat{c}} = \boldsymbol{G} \boldsymbol{\hat{a}} | ||
|
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