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Hubbard Model
·
Module 3
Formulation and Symmetries of the Hubbard Model
1
On-Site Coulomb Repulsion in Tight-Binding Models
State the physical motivation for including on-site Coulomb repulsion in the tight-binding model.
2
Hubbard Model: Hopping and Interaction
Write the Hubbard model Hamiltonian and identify the roles of the hopping parameter 't' and interaction parameter 'U'.
3
Hubbard Model: Interaction and Double Occupancy
Express the Hubbard interaction term using number operators and interpret double occupancy physically.
4
Regimes of the Hubbard Model
Characterize the weak coupling (U ≪ t), strong coupling (U ≫ t), and half-filling regimes and describe their expected physical behavior.
5
Spin-Rotation Symmetry of the Hubbard Model
Show that the total spin operator commutes with the Hubbard Hamiltonian, establishing SU(2) spin-rotation symmetry.
Particle-Hole Symmetry on a Bipartite Lattice
Derive the particle-hole transformation and show that the model has particle-hole symmetry on a bipartite lattice at half-filling.
Previous module
The Tight-Binding Model
Next module
Exact Solution of the Two-Site Hubbard Model