triqs_modest.misc.IbzSymmetryOps

class triqs_modest.misc.IbzSymmetryOps

Irreducible Brillouin Zone (IBZ) symmetry operations to symmetrize observables over the entire Brillouin zone.

The IBZ symmetry operations are optional and specific to DFT codes that work in the IBZ instead of the full BZ. Currently, this is only used when DFT data is converted from Wien2k.

For computational efficiency, we can perform the one-body calculation on the irreducible Brillouin zone (IBZ). However, in order to obtain observable quantities like the local Green’s function, one needs to _symmetrize_ the obversable summed on only the IBZ. For any observable \(\mathcal{O}\), the unsymmetrized quantity is

\[[\mathcal{O}^{\sigma}_{mm'}]_{\mathrm{unsymm}} = \sum_{\mathbf{k}\in\mathrm{IBZ}}\sum_{\nu\nu'}P_{m,\nu}^{\sigma} (\mathbf{k})O_{\nu\nu'}^{\sigma}(\mathbf{k})[P_{m'\nu'}^{\sigma}(\mathbf{k})]^{\dagger}.\]

To symmetrize, we must by apply all operations symmetry operations \(\mathcal{S}\) of the crystallographic space group \(\mathcal{G}\):

\[[\mathcal{O}^{\sigma}_{(am_{a}), (a'm_{a}')}]_{\mathrm{symm}}^{\mathcal{G}} = \sum_{\mathcal{S}\in\mathcal{G}} \sum_{n_{a}n_{a}'} \mathcal{D}_{m_{a} n_{a}}(\mathcal{S})[(\mathcal{O}^{\mathcal{S}^{-1}a,\mathcal{S}^{-1} \sigma})_{n_{a}n_{a}'}]_{\mathrm{unsymm}}\mathcal{D}(\mathcal{S}^{-1})_{n_{a}'m_{a}'}.\]

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Synthesized constructor with the following keyword arguments:

Parameters:

ops[Op]

Attributes

ops