triqs.atom_diag.atom_diag.atomic_density_matrix

triqs.atom_diag.atom_diag.atomic_density_matrix()

Dispatched C++ function(s).

[1] (atom: AtomDiagReal, beta: float)
  -> [ndarray[float, 2]]

[2] (atom: AtomDiagComplex, beta: float)
  -> [ndarray[complex, 2]]

Compute the atomic density matrix at inverse temperature \(\beta\).

Returns the Gibbs density matrix \(\hat\rho = e^{-\beta \hat H} / Z\) as a block-diagonal matrix, with one diagonal block per invariant subspace \(B\). The density matrix is expressed in the eigenbasis, hence each block is itself diagonal,

\[\rho_B = \mathrm{diag}\!\Bigl( e^{-\beta E_{B,i}} / Z \Bigr)_{i=0}^{\dim(B)-1}.\]

Parameters:

atomAtomDiagReal, AtomDiagComplex

Solved diagonalization problem.

betafloat

Inverse temperature \(\beta > 0\).

Returns:

[1][ndarray[float, 2]]

Gibbs density matrix of the system, as a list of diagonal blocks indexed by subspace index \(B\).

[2][ndarray[complex, 2]]

Gibbs density matrix of the system, as a list of diagonal blocks indexed by subspace index \(B\).