# Introduction to the QSGW+DMFT tutorials

The general framework of the QSGW+DMFT method (true also for LDA+DMFT) relies on a separation of the whole problem into a lattice and an impurity problem. The solution of the joint problem is found by repeatedly hopping from one picture to the other, using the output of one calculation to improve the input of the successive at every iteration. Projection and embedding operations allow for transitions from one picture to the other.

The solution of each of the two pictures relies on a self-consistent procedure. For the lattice problem it is the QSGW loop (see dedicated tutorials), whereas for the impurity picture we speak about the DMFT loop. The two loops are closed in a larger loop (so called ‘density loop’) that allows for a fully self-consistent description. A schematic representation is depicted in the figure below.

The following tutorials will guide you in the solution of the DMFT loop and the density loop. It’s assumed that you understand how to perform a QSGW loop and what are the basic input/output of QSGW. If this is not the case, please rely on dedicated tutorials.

### Structure of this tutorial section

- The first tutorial is about the maniupulations to be done on the QSGW ouput to start the DMFT loop. Here you can also find input files that will be used throughout all tutorials.
- The second tutorial is about how to perform a DMFT loop until convergence.
- The third one is about possible errors and some indications and rules-of-thumb to set and adjust the input parameters of the DMFT loop.
- The fourth tutorial is about how to close the density loop by means of the charge+static-magnetic approach.
- The fifth tutorial is about how to close the density loop by updating the density with the dynamical approach (standard method).
- The sixth tutorial focuses on the maximum entropy method, used to analytically continue the self-energy from the Matsubara’s frequency mesh to the real frequency axis.
- The seventh tutorial is about how to close the external loop by updating the self-energy instead of the density. It also contains a section about how to construct the dynamical double-counting.

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