risb.embedding.embedding_atom_diag module¶

Embedding solver using TRIQS AtomDiag.

class risb.embedding.embedding_atom_diag.EmbeddingAtomDiag(h_int, gf_struct)[source]¶

Bases: object

Impurity solver of embedding space using triqs.atom_diag.AtomDiag from TRIQS.

Parameters:

h_int (triqs.operators.Operator) – Interaction Hamiltonian in the embedding space.
gf_struct (list of pairs [ (str,int), ...]) – Structure of the matrices. It must be a list of pairs, each containing the name of the matrix block as a string and the size of that block. For example: [ ('up', 3), ('down', 3) ].

ad¶: The TRIQS AtomDiag instance. See triqs.atom_diag.AtomDiag in the TRIQS manual.

get_rho_c(bl)[source]¶

Return c-electron density matrix.

Parameters:: bl (str) – Which block in gf_struct to return.
Returns:: The c-electron density matrix rho_c from impurity.
Return type:: numpy.ndarray

get_rho_cf(bl)[source]¶

Return the cf hybridization (off-diagonal) density matrix.

Parameters:: bl (str) – Which block in gf_struct to return.
Returns:: The c,f-electron hybridization density matrix rho_cf from impurity.
Return type:: numpy.ndarray

get_rho_f(bl)[source]¶

Return f-electron densitym atrix.

Parameters:: bl (str) – Which block in gf_struct to return.
Returns:: The f-electron density matrix rho_f from impurity.
Return type:: numpy.ndarray

gf_struct¶

Block matrix structure of c-electrons.

Type:: dict[tuple[str,int]]

gf_struct_bath¶

Block matrix structure of f-electrons.

Type:: dict[tuple[str,int]]

gf_struct_emb¶

Block matrix structure entire embedding space.

Type:: dict[tuple[str,int]]

property gs_energy¶: Return ground state energy of impurity problem.

gs_vector¶

Ground state of the embedding problem.

Type:: triqs.atom_diag.AtomDiag vacuum

h0_loc¶

Single-particle quadratic couplings of c-electron terms in :h_emb.

Type:: triqs.operators.Operator

h_bath¶

Bath terms in h_emb.

Type:: triqs.operators.Operator

h_emb¶

Embedding Hamiltonian. It is the sum of h0_loc, h_int, h_hybr, and h_bath.

Type:: triqs.operators.Operator

h_hybr¶

Hybridization terms in h_emb.

Type:: triqs.operators.Operator

h_int¶

Interaction Hamiltonian.

Type:: triqs.operators.Operator

overlap(Op, force_real=True)[source]¶

Calculate the expectation value of an operator against the ground state of the embedding problem.

Parameters:

Op (triqs.operators.Operator) – Operator to take expectation of.
force_real (bool, optional) – Whether the result should be real or complex.

Returns:

Expectation value.

Return type:

triqs.operators.Operator

rho_c¶

c-electron density matrix.

Type:: dict[numpy.ndarray]

rho_cf¶

Density matrix of hybridization terms (c- and f-electrons).

Type:: dict[numpy.ndarray]

rho_f¶

f-electron density matrix.

Type:: dict[numpy.ndarray]

set_h0_loc(h0_loc_matrix)[source]¶

Set the single-particle quadratic couplings of the c-electrons in the embedding Hamiltonian.

Parameters:: h0_loc_matrix (dict of ndarray, optional) – Quadratic terms as a matrix. Each key in dictionary must follow gf_struct.

set_h_bath(Lambda_c)[source]¶

Set the bath terms in the impurity Hamiltonian.

Parameters:: Lambda_c (dict of ndarray, optional) – Bath coupling. Each key in dictionary must follow gf_struct.

set_h_emb(Lambda_c, D, h0_loc_matrix=None, mu=None)[source]¶

Set the terms in the impurity Hamiltonian to solve the embedding problem.

Parameters:

Lambda_c (dict[numpy.ndarray]) – Bath coupling. Each key in dictionary must follow gf_struct.
D (dict[numpy.ndarray]) – Hybridization coupling. Each key in dictionary must follow gf_struct.
h0_loc_matrix (dict[numpy.ndarray], optional) – Single-particle quadratic couplings of the c-electrons. Each key in dictionary must follow gf_struct.

set_h_hybr(D)[source]¶

Set the hybridization terms in the impurity Hamiltonian.

Parameters:: D (dict[numpy.ndarray]) – Hybridization coupling. Each key in dictionary must follow gf_struct.

set_h_int(h_int)[source]¶

Set the interaction terms of the c-electrons in the embedding Hamiltonian.

Parameters:: h_int (triqs.operators.Operator) – Interaction Hamiltonian in the embedding space.

solve()[source]¶: Solve for the groundstate in the half-filled number sector of the embedding problem.