The band gap opens up at low temperatures due to hybridization of localized electrons (mostly f-electrons) with conduction electrons, a correlation effect known as Kondo effect.
This explained why metal samples containing magnetic impurities have a resistance minimum (see Kondo effect).
The magnetic impurity can then interact with the conduction electrons of the metal, leading to interesting physics such as the Kondo effect, and heavy fermion behaviour.
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The DMRG has been successfully applied to get the low energy properties of spin chains: Ising model in a transverse field, Heisenberg model, etc., fermionic systems, such as the Hubbard model, problems with impurities such as the Kondo effect, boson systems, and the physics of quantum dots joined with quantum wires.