Understanding correlations and localization in the Hubbard model ...

The Hubbard model
Breakdown of band theory: correlation
Hamiltonian:
H =
hopping H t
{ }} {
−t ∑
{c † i,σ c j,σ + H.c.} +
〈i,j〉σ
interaction H
{ }} { U
U ∑ n i↑ n i↓
i
Limiting cases: Mott metal-insulator transition
Exact solution known in 1D via Bethe ansatz (Lieb
and Wu, 1968): insulator for finite U.
High-T c superconductivity
Understanding correlations and localization in the Hubbard model from variational calculations – p. 4