Interaction Hamiltonians
ModEST provides factory functions that build a local interaction Hamiltonian as a TRIQS many-body operator on the flavors of the impurity problem. The generic form is
\[\begin{split}H_{\mathrm{int}} =
\frac{1}{2} \sum_{\substack{\alpha\beta\gamma\delta \\ \sigma\sigma'}}
U_{\alpha\beta\gamma\delta}\;
c^{\dagger}_{\alpha\sigma}\, c^{\dagger}_{\beta\sigma'}\,
c_{\delta\sigma'}\, c_{\gamma\sigma},\end{split}\]
where \(\alpha,\beta,\gamma,\delta\) index the orbitals of the
impurity, \(\sigma,\sigma'\) are spin (or block-diagonal) indices,
and \(U_{\alpha\beta\gamma\delta}\) is the matrix of two-particle
interactions. The factories below differ in how
\(U_{\alpha\beta\gamma\delta}\) is parametrized — density–density
only, Kanamori, or full rotationally-invariant Slater — and return a
triqs.operators.Operator ready to be handed to a TRIQS impurity
solver.
Construct a density-density interaction Hamiltonian. |
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Construct a Hubbard-Kanamori Hamiltonian. |
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Construct a Slater Hamiltonian. |