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matteodalessio98 authored Mar 11, 2024
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# Yambo tutorial: Quasiparticles in the GW approximation

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**Useful info for the tutorial:**
**Useful info for the tutorial:**

- __Please download the directory containing the tutorial [HERE]([MoS2_HPC_tutorial.tar.gz](https://media.yambo-code.eu/educational/tutorials/files/MoS2_HPC_tutorial_Leonardo.tar.gz))__ and copy it in your user directory.
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- __Please download the directory containing the tutorial [HERE]([MoS2_HPC_tutorial.tar.gz](https://media.yambo-code.eu/educational/tutorials/files/MoS2_HPC_tutorial_Leonardo.tar.gz))__ and copy it in your user directory.

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In this tutorial you will learn how to run a GW simulation using Yambo on a HPC machine.

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We want to describe the electronic energy levels using a better description of electron-electron interactions than DFT is capable of.

Essentially, we want to solve the non-linear quasiparticle equation at first order in the GW self-energy $\Sigma$:
Essentially, we want to solve the non-linear quasiparticle equation at first order in the GW self-energy {math}`Σ`:

```math
```{math}
E^{QP}_{nk}=\epsilon_{nk}+Z_{nk}[\Sigma]\langle\psi_{nk}|\Sigma(\epsilon_{nk})-V_{xc}|\psi_{nk}\rangle
```

Here $\epsilon_{nk}$ and $\psi_{nk}$ are the Kohn-Sham energies and wavefunctions, respectively, while $V_{xc}$ is the DFT exchange-correlation potential.
Here {math}`\epsilon_{nk}` and {math}`\psi_{nk}` are the Kohn-Sham energies and wavefunctions, respectively, while $V_{xc}$ is the DFT exchange-correlation potential.

For each electronic state $nk$, the self-energy can be separated into two components: a static, gap-opening term called the exchange self-energy ($\Sigma^x$), and an energy-dependent, usually gap-closing term called the correlation self-energy ($\Sigma^c$). These contributions are tackled separately by the code:

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