Desert (particle physics)
In the Grand Unified Theory of particle physics, the desert refers to a theorized gap in energy scales, between the TeV scale and the GUT scale, in which no unknown interactions appear.
It can also be described as a gap in the lengths involved, with no new physics below 10−18 m (the currently probed length scale) and above 10−31 m (the GUT length scale).
The idea of the desert was motivated by the observation of approximate, order of magnitude, gauge coupling unification at the GUT scale. Adding interactions at an intermediate scale generically disrupts the gauge coupling unification.
The Hubbard model is an approximate model used, especially in solid-state physics, to describe the transition between conducting and insulating systems. The Hubbard model, named after John Hubbard, is the simplest model of interacting particles in a lattice, with only two terms in the Hamiltonian (see example below): a kinetic term allowing for tunneling ("hopping") of particles between sites of the lattice and a potential term consisting of an on-site interaction. The particles can either be fermions, as in Hubbard's original work, or bosons, when the model is referred to as either the "Bose–Hubbard model" or the "boson Hubbard model".
The Hubbard model is a good approximation for particles in a periodic potential at sufficiently low temperatures that all the particles are in the lowest Bloch band, as long as any long-range interactions between the particles can be ignored.
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