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The Hubbard model - an introduction and selected rigorous results

1998; IOP Publishing; Volume: 10; Issue: 20 Linguagem: Inglês

10.1088/0953-8984/10/20/004

1361-648X

Hal Tasaki,

Advanced Chemical Physics Studies

The Hubbard model is a `highly oversimplified model' for electrons in a solid which interact with each other through extremely short-ranged repulsive (Coulomb) interaction. The Hamiltonian of the Hubbard model consists of two parts: which describes quantum mechanical hopping of electrons, and which describes non-linear repulsive interaction. Either or alone is easy to analyse, and does not favour any specific order. But their sum is believed to exhibit various non-trivial phenomena including metal-insulator transition, antiferromagnetism, ferrimagnetism, ferromagnetism, Tomonaga-Luttinger liquid, and superconductivity. It is believed that we can find various interesting `universality classes' of strongly interacting electron systems by studying the idealized Hubbard model.