BMBPT Diagram¶

Routines and class for Bogoliubov MBPT diagrams.

class adg.bmbpt.BmbptFeynmanDiagram(nx_graph, tag_num)[source]¶

Bases: Diagram

Describes a BMBPT Feynman diagram with its related properties.

Parameters

nx_graph (NetworkX MultiDiGraph) – The graph of interest.
tag_num (int) – The tag number associated to the diagram.

attribute_expressions(time_diag)[source]¶

Attribute the correct Feynman and Goldstone expressions.

Parameters: time_diag (TimeStructureDiagram) – The associated TSD.

attribute_qp_labels()[source]¶: Attribute the appropriate qp labels to the graph’s propagators.

degrees¶

The ascendingly sorted degrees of the graph vertices.

Type: tuple

diag_exp¶

The Goldstone expression associated to the diagram.

Type: str

equivalent_permutations()[source]¶

Return the permutations generating equivalent diagrams.

Returns: Vertices permutations as dictionnaries.
Return type: list

extract_integral()[source]¶

Return the integral part of the Feynman expression of the diag.

Returns: The integral part of its Feynman expression.
Return type: str

extract_numerator()[source]¶

Return the numerator associated to a BMBPT graph.

Returns: The numerator of the graph.
Return type: str

feynman_exp¶

The Feynman expression associated to the diagram.

Type: str

graph¶

The actual graph.

Type: NetworkX MultiDiGraph

has_crossing_sign()[source]¶

Return True for a minus sign associated with crossing propagators.

Use the fact that all lines propagate upwards and the canonical representation of the diagrams and vertices.

Returns

Encode for the sign factor associated with crossing: propagators.

Return type

bool

has_sign_factor()[source]¶

Return True if a sign factor is associated to the diagram.

Wrapper allowing for easy refactoring of expression code.

Returns: The presence of a sign factor.
Return type: bool

hf_type¶

The Hartree-Fock, non-Hartree-Fock or Hartree-Fock for the energy operator only character of the graph.

Type: str

io_degrees¶

The sorted version of unsort_io_degrees.

Type: tuple

max_degree¶

The maximal degree of a vertex in the graph.

Type: int

multiplicity_symmetry_factor()[source]¶

Return the symmetry factor associated with propagators multiplicity.

Returns: The symmetry factor associated with equivalent lines.
Return type: str

symmetry_factor()[source]¶

Return the overall symmetry factor of the diagram.

Returns: The combination of all symmetry factors.
Return type: str

tags¶

The tag numbers associated to a diagram.

Type: list

time_tag¶

The tag number associated to the diagram’s associated TSD.

Type: int

time_tree_denominator(time_graph)[source]¶

Return the denominator for a time-tree graph.

Parameters: time_graph (NetworkX MultiDiGraph) – Its associated time-structure graph.
Returns: The denominator of the graph.
Return type: str

tsd_is_tree¶

The tree or non-tree character of the associated TSD.

Type: bool

two_or_three_body¶

The 2 or 3-body characted of the vertices.

Type: int

unique_id¶

A unique number associated to the diagram.

Type: int

unsort_degrees¶

The degrees of the graph vertices

Type: tuple

unsort_io_degrees¶

The list of in- and out-degrees for each vertex of the graph, stored in a (in, out) tuple.

Type: tuple

vert_exp¶

The expression associated to the vertices.

Type: list

property vertex_exchange_sym_factor¶

Return the symmetry factor associated with vertex exchange.

Returns: The symmetry factor for vertex exchange.
Return type: int

vertex_expression(vertex)[source]¶

Return the expression associated to a given vertex.

Parameters: vertex (int) – The vertex of interest in the graph.
Returns: The LaTeX expression associated to the vertex.
Return type: str

write_diag_exps(latex_file, norder)[source]¶

Write the expressions associated to a diagram in the LaTeX file.

Parameters

latex_file (file) – The LaTeX outputfile of the program.
norder (int) – The order in BMBPT formalism.

write_graph(latex_file, directory, write_time)[source]¶

Write the BMBPT graph and its associated TSD to the LaTeX file.

Parameters

latex_file (file) – The LaTeX output file of the program.
directory (str) – The path to the result folder.
write_time (bool) – True if we want informations on the associated TSDs.

write_section(result, commands, section_flags)[source]¶

Write section and subsections for BMBPT result file.

Parameters

result (file) – The LaTeX output file of the program.
commands (dict) – The flags associated with run management.
section_flags (dict) – UniqueIDs of diags starting each section.

write_tsd_info(diagrams_time, latex_file)[source]¶

Write info related to the BMBPT associated TSD to the LaTeX file.

Parameters

diagrams_time (list) – The associated TSDs.
latex_file (file) – The LaTeX output file of the program.

write_vertices_values(latex_file, mapping)[source]¶

Write the qp energies associated to each vertex of the diag.

Parameters

latex_file (file) – The LaTeX output file of the program.
mapping (dict) – A mapping between the vertices in the diagram and the vertices in its euivalent TSD, since permutations between vertices are possible.

adg.bmbpt.check_topologically_equivalent(matrices, max_vertex)[source]¶

Exclude matrices that would spawn topologically equivalent graphs.

Parameters

matrices (list) – Adjacency matrices to be checked.
max_vertex (int) – The maximum vertex which have been filled.

Returns

The topologically unique matrices.

Return type

list

>>> import numpy
>>> mats = [numpy.array([[0, 2, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]]),                 numpy.array([[0, 0, 2, 0], [0, 0, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0]])]
>>>
>>> mats = check_topologically_equivalent(mats, 2)
>>> mats 
[array([[0, 2, 0, 0], [2, 0, 0, 1], [0, 0, 0, 0], [0, 0, 0, 0]])]
>>>
>>> mats = check_topologically_equivalent([], 2)
>>> mats 
[]

adg.bmbpt.check_unconnected_spawn(matrices, max_filled_vertex)[source]¶

Exclude some matrices that would spawn unconnected diagrams.

Do several permutations among the rows and columns corresponding to already filled vertices, and check if one obtains a block-diagonal organisation, where the off-diagonals blocks connecting the already-filled and yet-unfilled parts of the matrix would be empty. In that case, remove the matrix.

Parameters

matrices (list) – The adjacency matrices to be checked.
max_filled_vertex (int) – The furthest vertex until which the matrices have been filled.

>>> import numpy
>>> mats = [numpy.array([[0, 2, 0], [2, 0, 0], [0, 0, 0]]),                 numpy.array([[0, 2, 1], [2, 0, 1], [0, 0, 0]])]
>>>
>>> check_unconnected_spawn(mats, 1)
>>> mats 
[array([[0, 2, 1], [2, 0, 1], [0, 0, 0]])]

adg.bmbpt.diagrams_generation(p_order, three_body_use, nbody_obs, canonical)[source]¶

Generate diagrams for BMBPT from bottom up.

Parameters

p_order (int) – The BMBPT perturbative order of the studied diagrams.
three_body_use (bool) – Flag for the use of three-body forces.
nbody_obs (int) – N-body character of the obervable of interest.
canonical (bool) – True if one draws only canonical diagrams.

Returns

NumPy arrays encoding the adjacency matrices of the graphs.

Return type

list

>>> diags = diagrams_generation(1, False, 2, False)
>>> len(diags)
2
>>> any(np.array_equal([[0, 4], [0, 0]], diag) for diag in diags)
True
>>> any(np.array_equal([[0, 2], [0, 0]], diag) for diag in diags)
True
>>> diags = diagrams_generation(1, True, 3, False)
>>> len(diags)
3
>>> any(np.array_equal([[0, 6], [0, 0]], diag) for diag in diags)
True
>>> any(np.array_equal([[0, 4], [0, 0]], diag) for diag in diags)
True
>>> any(np.array_equal([[0, 2], [0, 0]], diag) for diag in diags)
True
>>> diags = diagrams_generation(2, False, 2, True)
>>> len(diags)
2
>>> any(np.array_equal([[0, 2, 2], [0, 0, 2], [0, 0, 0]], d) for d in diags)
True
>>> any(np.array_equal([[0, 1, 1], [0, 0, 3], [0, 0, 0]], d) for d in diags)
True

adg.bmbpt.order_and_remove_topologically_equiv(matrices, max_vertex)[source]¶

Order the matrices in sub-list and remove topologically equivalent ones.

Parameters

matrices (list) – The adjacency matrices to be checked.
max_vertex (int) – The maximum vertex which has been filled.

Returns

The ordered topologically unique matrices.

Return type

list

adg.bmbpt.order_diagrams(diagrams)[source]¶

Order the BMBPT diagrams and return number of diags for each type.

Parameters

diagrams (list) – Possibly redundant BmbptFeynmanDiagrams.

Returns

First element is the list of topologically unique, ordered: diagrams. Second element is a dict with the number of diagrams for each major type. Third element is a dict with the identifiers of diagrams starting each output file section.

Return type

tuple

adg.bmbpt.produce_expressions(diagrams, diagrams_time)[source]¶

Produce and store the expressions associated to the BMBPT diagrams.

Parameters

diagrams (list) – The list of all BmbptFeynmanDiagrams.
diagrams_time (list) – Their associates TSDs.

adg.bmbpt.remove_disconnected_matrices(matrices)[source]¶

Remove matrices corresponding to disconnected diagrams.

Parameters: matrices (list) – List of adjacency matrices.

adg.bmbpt.write_header(tex_file, commands, diags_nbs)[source]¶

Write overall header for BMBPT result file.

Parameters

tex_file (file) – The ouput LaTeX file of the program.
commands (Namespace) – Flags for the program run.
diags_nbs (dict) – The number of diagrams per type.