diff --git a/content/day5/yambo-tutorial.md b/content/day5/yambo-tutorial.md index f987041..c3a2413 100644 --- a/content/day5/yambo-tutorial.md +++ b/content/day5/yambo-tutorial.md @@ -1,13 +1,14 @@ .. - _day5-yambo: + _day5-yambo: # Yambo tutorial: Quasiparticles in the GW approximation .. - **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. +.. + - __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. In this tutorial you will learn how to run a GW simulation using Yambo on a HPC machine. @@ -25,13 +26,13 @@ In the end, you will obtain a quasiparticle band structure based on the simulati 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: