triqs_modest.embedding.Embedding.embed

Embedding.embed()

Dispatched C++ function(s).

[1] (imps_blocks: [[ndarray[complex, 2]]])
  -> [ndarray[complex, 2]]

[2] (imps_blocks: [[ndarray[complex, 3]]])
  -> [ndarray[complex, 3]]

[3] (imps_blocks: [[ndarray[complex, 4]]])
  -> [ndarray[complex, 4]]

[4] (imps_blocks: [[ndarray[complex, 5]]])
  -> [ndarray[complex, 5]]

[5] (Sigma_imp_vec: [BlockGf[MeshImFreq, 2]])
  -> Block2Gf[MeshImFreq, 2]

[6] (Sigma_imp_vec: [BlockGf[MeshReFreq, 2]])
  -> Block2Gf[MeshReFreq, 2]

[7] (Sigma_imp_vec: [BlockGf[MeshDLRImFreq, 2]])
  -> Block2Gf[MeshDLRImFreq, 2]

[8] (Sigma_imp_vec: [BlockGf[MeshImFreq, 2]],
     Sigma_imp_static_vec: [[ndarray[complex, 2]]])
  -> tuple[Block2Gf[MeshImFreq, 2], ndarray[ndarray[complex, 2], 2]]

[9] (Sigma_imp_vec: [BlockGf[MeshReFreq, 2]],
     Sigma_imp_static_vec: [[ndarray[complex, 2]]])
  -> tuple[Block2Gf[MeshReFreq, 2], ndarray[ndarray[complex, 2], 2]]

[10] (Sigma_imp_vec: [BlockGf[MeshDLRImFreq, 2]],
     Sigma_imp_static_vec: [[ndarray[complex, 2]]])
  -> tuple[Block2Gf[MeshDLRImFreq, 2], ndarray[ndarray[complex, 2], 2]]

[11] (Sigma_imp_static_vec: [[ndarray[complex, 2]]])
  -> ndarray[ndarray[complex, 2], 2]

[1, 2, 3, 4] Embed impurity data into the full correlated space.

This method maps impurity solver data into the embedded representation using the \(\psi\) mapping table. Given data from each impurity solver organized by blocks \((\gamma, \tau)\), the method constructs the full embedded arrays indexed by \((\alpha, \sigma)\).

The algorithm proceeds as follows: 1. Initialize zero arrays for each \((\alpha, \sigma)\) block with dimensions from

sigma_embed_decomp.

2. For each \((\alpha, \sigma)\), look up \(\psi(\alpha, \sigma) = (n\_imp, \gamma, \tau)\) and copy the corresponding impurity block data.

3. Assemble the blocks into full diagonal tensors for each spin channel \(\sigma\).

Blocks with imp_idx == -1 (disconnected from any impurity) remain zero.

The template parameter Rank determines the dimensionality of the data arrays. For frequency-dependent quantities (Rank ∈ {3,5}), the first dimension is the frequency index.

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[5, 6, 7] Embed Green’s function containers.

Embed impurity solver self-energies into an embedded self-energy.

• \(\Sigma_{\text{embed}}^{ασ} = \Sigma_{\text{imp}}^{ψ(α,σ)}\),

• \(\psi(\alpha,\sigma) \to\) (n_imp, \(\gamma\), \(\tau\)).

---

[8, 9, 10] Embed pairs Green’s function containers and matrices.

Embed the impurity self-energy decomposed as a list of dynamic and a list of static parts.

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[11] Embed block matrices into the full correlated space.

Embeds static (frequency-independent) impurity data stored as block matrices into the \((\alpha, \sigma)\)-indexed embedded representation. This is the matrix analogue of the frequency-dependent embed operation.

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Parameters:

imps_blocks[[ndarray[complex, 2]]], [[ndarray[complex, 3]]], [[ndarray[complex, 4]]], [[ndarray[complex, 5]]]

Nested vector [n_imp][block] of impurity data arrays.

Sigma_imp_vec[BlockGf[MeshImFreq, 2]], [BlockGf[MeshReFreq, 2]], [BlockGf[MeshDLRImFreq, 2]]

A list of impurity self-energies.

Sigma_imp_static_vec[[ndarray[complex, 2]]]

A list of static impurity self-energies.

Returns:

[1][ndarray[complex, 2]]

Vector of embedded arrays, one per spin channel \(\sigma\).

[2][ndarray[complex, 3]]

Vector of embedded arrays, one per spin channel \(\sigma\).

[3][ndarray[complex, 4]]

Vector of embedded arrays, one per spin channel \(\sigma\).

[4][ndarray[complex, 5]]

Vector of embedded arrays, one per spin channel \(\sigma\).

[5]Block2Gf[MeshImFreq, 2]

\(\Sigma_{\text{embed}}[\alpha, \sigma]\) in \(\mathcal{C}\) space using the embed decomposition.

[6]Block2Gf[MeshReFreq, 2]

\(\Sigma_{\text{embed}}[\alpha, \sigma]\) in \(\mathcal{C}\) space using the embed decomposition.

[7]Block2Gf[MeshDLRImFreq, 2]

\(\Sigma_{\text{embed}}[\alpha, \sigma]\) in \(\mathcal{C}\) space using the embed decomposition.

[8]tuple[Block2Gf[MeshImFreq, 2], ndarray[ndarray[complex, 2], 2]]

The self-energy in the \(\mathcal{C}\) space as a pair (dynamic, static).

[9]tuple[Block2Gf[MeshReFreq, 2], ndarray[ndarray[complex, 2], 2]]

The self-energy in the \(\mathcal{C}\) space as a pair (dynamic, static).

[10]tuple[Block2Gf[MeshDLRImFreq, 2], ndarray[ndarray[complex, 2], 2]]

The self-energy in the \(\mathcal{C}\) space as a pair (dynamic, static).

[11]ndarray[ndarray[complex, 2], 2]

Embedded block2 matrix in \(\mathcal{C}\) space.