Anderson orthogonality theorem

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Anderson orthogonality theorem

In a metal, adding a localized impurity (like a magnetic impurity) changes how the electrons move. The ground state of all electrons with no impurity and the ground state with the impurity become orthogonal when the system size goes to infinity. In simple terms, the many-electron state before the impurity and the state after the impurity are completely different for a very large metal.

Why this happens: the conduction electrons rearrange themselves to screen the impurity. With a huge number of electrons, this rearrangement changes the overall many-body wavefunction so much that the two states have essentially zero overlap.

This zero overlap in the thermodynamic limit is called the Anderson orthogonality catastrophe and has important consequences in fields like spectroscopy and quantum dynamics.