.states — Exciton Eigenstates

The .states file (written with the -c / --eigenstates flag) contains the complex coefficients $A^{Q}_{vc}(\mathbf{k})$ that define each exciton wavefunction in the electron–hole basis. These are exactly the amplitudes that appear in the Bethe‑Salpeter Equation (see Eq. 14 of the paper):

\[(\varepsilon_{c,\mathbf{k+Q}} - \varepsilon_{v,\mathbf{k}}) A^{Q}_{vc}(\mathbf{k}) + \sum_{v'c'\mathbf{k}'} K_{vc,v'c'}(\mathbf{k},\mathbf{k}',Q)\, A^{Q}_{v'c'}(\mathbf{k}') \;=\; E_X\,A^{Q}_{vc}(\mathbf{k})\]

File Structure

Header line
```
n_pairs
```
The dimension n_pairs of the BSE matrix – i.e. the total number of distinct electron-hole pairs $(v,c,\mathbf{k})$ used for the calculation.
Basis definition (next ``n_pairs`` lines)

Each line lists one electron–hole pair in the exact order used later for the coefficients:
```
k_x   k_y   k_z   v   c
```
$k_x\quad k_y\quad k_z\quad$ are given in crystal‑momentum units (fractional coordinates or $Å^{-1}$, depending on input), $v$ and $c$ are valence and conduction band indices.
Exciton coefficient matrix

After the basis section, each remaining line corresponds to one exciton state. The coefficients are written as consecutive real–imaginary pairs following the same ordering of electron–hole pairs defined above:
```
Re(A1)  Im(A1)  Re(A2)  Im(A2)  ...  Re(An)  Im(An)
.
.
.
Re(A1)  Im(A1)  Re(A2)  Im(A2)  ...  Re(An)  Im(An)
```
where n = n_pairs. If you requested N exciton states with --states N (default=8), there will be N such lines.

Properties

Normalization Each row is normalized so that $\sum_{j=1}^{n_{\mathrm{pairs}}} |A_j|^2 = 1$.
Complex ordering The $j$-th complex pair in a row corresponds to the $j$-th electron–hole pair listed in the basis definition. This one‑to‑one mapping makes it straightforward to reconstruct the wavefunction in k‑space or transform it to real space.
Units The coefficients are dimensionless.