This title appears in the Scientific Report :
2019
The Many-Body Problem in Materials Science
The Many-Body Problem in Materials Science
The laws governing the electronic structure of materials known since long. The relevant equations are straightforward and pose no fundamental mathematical problems. Still they cannot be solved exactly given the resources of a finite universe. We will discuss the strategies that are used to deal with...
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Personal Name(s): | Koch, Erik (Corresponding author) |
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Contributing Institute: |
Jülich Supercomputing Center; JSC |
Imprint: |
2019
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Conference: | Condensed Matter Seminar, Zanjan (Iran), 2019-04-30 - |
Document Type: |
Talk (non-conference) |
Research Program: |
Computational Science and Mathematical Methods |
Publikationsportal JuSER |
The laws governing the electronic structure of materials known since long. The relevant equations are straightforward and pose no fundamental mathematical problems. Still they cannot be solved exactly given the resources of a finite universe. We will discuss the strategies that are used to deal with the many-body problem in practice. First we consider how the calculation of total energies can be reduced to density matrices and how this approach gives rise to density-functionals. After explaining when they work and when they fail, we return to the many-body wave-function. We show how they can be efficiently represented in second quantization and how they are implemented on the computer, giving the results of massively parallel Lanczos diagonalizations as practical examples. Finally, we will discuss how the treatment of correlated materials can be very efficiently handled using Dynamical Mean-Field Theory, which describes the solid as a correlated unit cell, embedded in a self-consistent dynamical medium. |