5. Gutzwiller Wavefunction methods
5.1. Theoretical background
Gutzwiller Wavefunction is defiend as
where \(\mathcal{P}\) is the local projector operator that improves the noninteracting wave function \(\ket{\Psi_0}\) according to the on-site interaction by modifying the weight of local electronic configurations:
where \(I\) is the index of site. \(\ket{I,\Gamma}\) denotes the local configurations of site \(I\).
Gutzwiller constraints:
where \(\hat{n}_I\) is the local single-particle density-matrix operator.
Symbols used in the documents:
\(\mathcal{N}\) is the number of sites
\(N_I\) is the number of orbitals in site \(I\).
\(I, J\) represent the indices of the fragments (or sites) of the system
\(\alpha, \beta, \gamma, \sigma\) denote the fermionic orbital.
\(\hat{T}_{IJ}\) is the hopping operator between two sites \(I, J\) and \(T_{I\alpha J\beta}\) is corresponding hopping integral
\(\hat{H}^{loc}_I\) represents the local Hamiltonain of site \(I\).
\(c_{Ip}, c^\dagger_{Iq}\) represents the original fermonic operator
\(f_{Ia}\) represents the auxiliary operator