magnopy.LSWT.GDM

method

LSWT.GDM(k, relative=False, units='meV')

Grand dynamical matrix.

Parameters:

k(3,) array-like

Reciprocal vector

relativebool, default False

If relative=True, then k is interpreted as given relative to the reciprocal unit cell. Otherwise it is interpreted as given in absolute coordinates.

unitsstr, default "meV"

Units of energy. See Units of energy for the full list of supported units.

Added in version 0.3.0.

Returns:

gdm(2M, 2M) numpy.ndarray

Gran dynamical matrix.

See also

LSWT.A

LSWT.B

Notes

Before the diagonalization, the magnon Hamiltonian has the form

\[\begin{split}\mathcal{H} = \dots + \sum_{\boldsymbol{k}, \alpha} \boldsymbol{\mathcal{A}}(\boldsymbol{k})^{\dagger} \begin{pmatrix} \boldsymbol{A}(\boldsymbol{k}) & \boldsymbol{B}^{\dagger}(\boldsymbol{k}) \\ \boldsymbol{B}(\boldsymbol{k}) & \overline{\boldsymbol{A}(-\boldsymbol{k})} \end{pmatrix} \boldsymbol{\mathcal{A}}(\boldsymbol{k})\end{split}\]

where

\[\boldsymbol{\mathcal{A}}(\boldsymbol{k}) = \begin{pmatrix} a_1(\boldsymbol{k}), \dots, a_M(\boldsymbol{k}), a^{\dagger}_1(-\boldsymbol{k}), \dots, a^{\dagger}_M(-\boldsymbol{k}), \end{pmatrix}\]

This function computes the grand dynamical matrix \(\boldsymbol{D}(\boldsymbol{k})\)

\[\begin{split}\boldsymbol{D}(\boldsymbol{k}) = \begin{pmatrix} \boldsymbol{A}(\boldsymbol{k}) & \boldsymbol{B}^{\dagger}(\boldsymbol{k}) \\ \boldsymbol{B}(\boldsymbol{k}) & \overline{\boldsymbol{A}(-\boldsymbol{k})} \end{pmatrix}\end{split}\]

Examples

>>> import magnopy
>>> spinham = magnopy.examples.cubic_ferro_nn()
>>> lswt = magnopy.LSWT(spinham=spinham, spin_directions=[[0, 0, 1]])
>>> lswt.GDM(k=[0,0,0.5], relative=True)
array([[1.+0.j, 0.-0.j],
       [0.+0.j, 1.-0.j]])