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Hubbard Model
·
Module 2
The Tight-Binding Model
1
Second Quantization and the Tight-Binding Hamiltonian
Construct the tight-binding Hamiltonian using second-quantized operators with site and spin indices.
2
Diagonalizing the Tight-Binding Hamiltonian
Diagonalize the tight-binding Hamiltonian by Fourier transforming to momentum-space operators to find the band structure.
3
Filling Fermions: The Non-Interacting Ground State
Construct the non-interacting ground state by filling momentum states up to the Fermi level.
4
Electron Density Calculation Using the Number Operator
Compute the expectation value of the number operator to determine the electron density at each site.
5
Kinetic Energy and Band Filling
Evaluate the kinetic energy of the non-interacting ground state as a function of band filling.
Previous module
Foundations of Second Quantization
Next module
Formulation and Symmetries of the Hubbard Model