Bose–Hubbard model

<p>The Bose–Hubbard model gives a description of the physics of interacting spinless <a href="/facts/Boson/XtPFcjb5">bosons</a> on a <a href="/facts/Lattice_model_(physics)/TY3bVAhk">lattice</a>. It is closely related to the <a href="/facts/Hubbard_model/5pphLNde">Hubbard model</a> that originated in <a href="/facts/Solid-state_physics/Cmc6hvyR">solid-state physics</a> as an approximate description of superconducting systems and the motion of electrons between the atoms of a <a href="/facts/Crystal/e2R2mk3E">crystalline solid</a>. The model was introduced by Gersch and Knollman in 1963 in the context of granular superconductors. (The term '<a href="/facts/Satyendra_Nath_Bose/rC6y84HS">Bose</a>' in its name refers to the fact that the particles in the system are <a href="/facts/Boson/XtPFcjb5">bosonic</a>.) The model rose to prominence in the 1980s after it was found to capture the essence of the superfluid-insulator transition in a way that was much more mathematically tractable than fermionic metal-insulator models.
</p><p>The Bose–Hubbard model can be used to describe physical systems such as bosonic atoms in an <a href="/facts/Optical_lattice/Inu8klUj">optical lattice</a>, as well as certain magnetic insulators. Furthermore, it can be generalized and applied to Bose–Fermi mixtures, in which case the corresponding <a href="/facts/Hamiltonian_(quantum_mechanics)/5XwK2HmD">Hamiltonian</a> is called the Bose–Fermi–Hubbard Hamiltonian.
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Bose–Hubbard model open-in-new

Bose–Hubbard model