Learning Dynamical Mean Field Theory

In summary, the speaker is a masters student who wants to apply DMFT to transport in strongly correlated systems. They have a basic understanding of the Hubbard model but want to learn DMFT in order to write their own code and solve toy problems. They are looking for a gentle introduction to DMFT and resources to help them develop simple programs. They have been recommended to check out Kristjan Haule's website and the ALPS project for DMFT code.
  • #1
maverick280857
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Hi,

I'm a masters student trying to apply DMFT to problems involving transport in strongly correlated systems. I have a cursory understanding of the physics behind the Hubbard model, which is to say, I have spent some time with it in a quantum many body theory course. However, I now want to learn DMFT to the point of being able to write my own DMFT code to solve a few toy problems before trying to figure out how to use it for non-equilibrium problems.

Could someone point me to a gentle introduction to DMFT which helps me develop some simple programs as well. I'm unable to find friendly references on the internet.

Thanks in advance!
 
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  • #2
There are a few codes you can find online, I think python scripts. You can probably reverse engineer them. I think Kristjan Haule's website has a few downloads, and there is also some DMFT code with the ALPS project.
 
  • #3
Thanks indeed OhYoungLions! That website looks like a very useful resource.
 

1. What is Dynamical Mean Field Theory (DMFT)?

Dynamical Mean Field Theory (DMFT) is a computational technique used to study the properties of strongly correlated materials, such as transition metal compounds and rare earth materials. It takes into account the local interactions between electrons, which is often the most dominant factor in these materials, and allows for the calculation of their electronic structure and dynamical properties.

2. How does DMFT differ from other theoretical methods?

DMFT is unique in that it treats the local interactions between electrons exactly, while approximating the effects of non-local interactions. This makes it particularly well-suited for studying strongly correlated materials, where local interactions play a crucial role. Unlike other theoretical methods, DMFT does not rely on any perturbative expansions and can be applied to a wide range of systems, including those with disorder and impurities.

3. What are the main applications of DMFT?

DMFT has been extensively used to study the electronic and magnetic properties of materials, including high-temperature superconductors, transition metal oxides, and heavy fermion systems. It has also been applied to problems in quantum chemistry, such as the calculation of Hubbard model parameters and the prediction of phase transitions.

4. What are some challenges associated with learning DMFT?

One of the main challenges in learning DMFT is the steep learning curve associated with understanding the underlying theoretical concepts and mathematical formalism. Another challenge is the computational complexity of implementing DMFT, which requires advanced programming skills and access to high-performance computing resources.

5. How can one get started with learning DMFT?

To get started with learning DMFT, it is recommended to have a strong foundation in theoretical physics and solid state physics. Familiarity with concepts such as many-body theory, Green's function, and statistical mechanics is also helpful. There are several textbooks and online resources available that provide a comprehensive introduction to DMFT, as well as tutorials and workshops that offer hands-on experience with implementing DMFT calculations.

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