Electronic structure methods | Electronic band structures

Peierls substitution

The Peierls substitution method, named after the original work by Rudolf Peierls is a widely employed approximation for describing tightly-bound electrons in the presence of a slowly varying magnetic vector potential. In the presence of an external magnetic vector potential , the translation operators, which form the kinetic part of the Hamiltonian in the tight-binding framework, are simply and in the second quantization formulation The phases are defined as (Wikipedia).

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Tight binding | Path integral formulation | Action (physics) | Hofstadter's butterfly