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Hubbard Model
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Module 4
Exact Solution of the Two-Site Hubbard Model
1
Fock Space Basis for Half-Filled Two-Site Hubbard Model
Enumerate all Fock space basis states for the two-site Hubbard model at half-filling.
2
Diagonalizing the Half-Filled Hamiltonian
Construct the Hamiltonian matrix in the half-filled sector and diagonalize it to obtain exact eigenvalues and eigenstates.
3
Ground State Crossover: Delocalization to Localization
Analyze the ground state as a function of U/t and identify the crossover from delocalized to localized behavior.
4
Double Occupancy in the Ground State: U/t Dependence
Calculate the double occupancy in the ground state as a function of U/t.
5
Singlet-Triplet Splitting and Antiferromagnetic Coupling
Identify the singlet-triplet energy splitting and relate it to an effective antiferromagnetic exchange coupling J.
6
Solving the Two-Site Model
Solve the two-site model for the case of a single electron and two electrons with parallel spins.
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