Model Pensona-Kolba-Hubbarda

The Penson-Kolb-Hubbard model, one of Hubbard's extensions, incorporates an additional expression in hamiltonian, derived from the Penson-Kolba model, which takes into account the electron pairs jumping between nodes. The hamiltonian is:

H ^ = ∑ i j & # x03C3; & # x2212; t i j c ^ j & # x03C3; & # x2020; c i & # x03C3; + U ∑ i c ^ i ↑ & # x2020; c i ↑ c i & # x2193; & # x2020; c i & # x2193; + J ∑ < i j > c j ↑ & # x2020; c j & # x2193; & # x2020; c i ↑ c i & # x2193; {\displaystyle {\hat {H}}=\sum _{ij\sigma }-t_{ij}{\hat {c}}_{j\sigma }^{\dagger }c_{i\sigma }+U\sum _{i}{\hat {c}}_{i\uparrow }^{\dagger }c_{i\uparrow }c_{i\downarrow }^{\dagger }c_{i\downarrow }+J\sum _{<ij>}c_{j\uparrow }^{\dagger }c_{j\downarrow }^{\dagger }c_{i\uparrow }c_{i\downarrow }}

The first two words correspond to the usual Hubbard model, while the last one comes from the Penson-Kolba model (as in the respective models).

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