# Calculating optical spectra including excitonic effects: a step-by-step guide

This tutorial guides you through the workflow of a calculation of the optical spectrum of a given material by solving the Bethe-Salpeter equation. Specifically we will use bulk h-BN as an example.

Before starting, you need to obtain the tarballs for hBN. See instructions on the main tutorials page.

The target quantity in a Bethe-Salpeter calculation is the macroscopic dielectric matrix ε_{M}. The following quantities/steps are needed to obtain ε_{M}:

The optical absorption spectrum corresponds to Imε_{M}(ω). Following this scheme we go through the flow of a calculation:

## Contents

### Step 1: Static screening

Use the *SAVE* folders that are already provided and do:

$ cd YAMBO_TUTORIALS/hBN/YAMBO

Follow the **Static screening** module and then **return to this tutorial **

### Step 2: Bethe-Salpeter kernel

Follow the module on **Bethe-Salpeter kernel** and **return to this tutorial**

### Step 3: Bethe-Salpeter solver

This is the final step in which you finally obtained the spectra. Mathematically this implies to solve a large eigenvalue problem. Two main solvers are available in yambo

(1) diagonalization of the full Hamiltonian (diagonalization solver)

(2) subspace iterative | Lanczos algorithm which by-pass diagonalization with the Haydock approach^{[1]} (Lanczos-Haydock solver)

For (1) follow the module on **Bethe-Salpeter solver: diagonalization** then either **return to this tutorial**
or follow the link to **Bethe-Salpeter solver: Lanczos-Haydock** for (2).

# References

- ↑ R. Haydock, in
*Solid State Phys.*,**35**215 (1980) edited by H. Ehrenfest, F. Seitz, and D. Turnbull, Academic Press