PBMBPT Diagram¶

Routines and class for Projected Bogoliubov MBPT diagrams.

class adg.pbmbpt.ProjectedBmbptDiagram(graph, unique_id, tag, child_tag)[source]¶

Bases: adg.bmbpt.BmbptFeynmanDiagram

Describes a PBMBPT diagram with its related properties.

two_or_three_body¶

The 2 or 3-body characted of the vertices.

Type:	int

time_tag¶

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

Type:	int

tsd_is_tree¶

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

Type:	bool

feynman_exp¶

The Feynman expression associated to the diagram.

Type:	str

diag_exp¶

The Goldstone expression associated to the diagram.

Type:	str

vert_exp¶

The expression associated to the vertices.

Type:	list

hf_type¶

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

Type:	str

unique_id¶

A unique number associated to the diagram.

Type:	int

vertex_exchange_sym_factor¶

Lazy-initialized symmetry factor associated to the vertex exchange, stored to avoid being computed several times.

Type:	int

check_graph¶

A copy of the graph that can be used for topological equivalence checks (lazy-initialized).

Type:	NetworkX MultiDiGraph

anomalous_contractions_factor()[source]¶

Return the factor associated with anomalous self-contractions.

Returns:	The anomalous self-contractions factor.
Return type:	(int)

attribute_expressions(time_diag)¶

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.

check_graph

Return a graph that can be used for topological equivalence checks.

Lazy-initialized to reduce memory and CPU costs as this operation requires a deep copy.

Returns:	The graph with doubled anomalous props.
Return type:	(NetworkX MultiDiGraph)

degrees¶

diag_exp

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 PBMBPT graph.

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

feynman_exp

graph¶

has_anom_non_selfcontracted_props()[source]¶

Return True if the diagram has anomalous propagators.

Returns:	The presence of anomalous propagators.
Return type:	(bool)

has_anom_props_linked_sign()[source]¶

Return True if there is a minus sign associated to anom props.

Anomalous propagators departing to higher vertices introduce a sign factor if a normal propagator is going to an even higher vertex, as it departs from the canonical representation used for numerator extraction.

Returns:	The presence of the sign factor.
Return type:	(bool)

has_crossing_sign()¶

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:	(boolean)

hf_type

io_degrees¶

max_degree¶

multiplicity_symmetry_factor()[source]¶

Return the symmetry factor associated with propagators multiplicity.

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

set_io_degrees()[source]¶: Attribute the correct in- and out-degrees to a PBMBPT diagram.

symmetry_factor()[source]¶

Return the overall symmetry factor of the diagram.

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

tags¶

time_tag

time_tree_denominator(time_graph)¶

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

two_or_three_body

unique_id

unsort_degrees¶

unsort_io_degrees¶

vert_exp

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 PBMBPT 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)¶

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)¶

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)¶

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.pbmbpt.equiv_generating_permutations(graph)[source]¶

Return the list of permutations generating equivalent PBMBPT diags.

adg.pbmbpt.graph¶

The graph to be checked.

Type:	Networkx MultiDiGraph

Returns:	The mappings giving equivalent graphs, inc. identity.
Return type:	(list)

adg.pbmbpt.filter_new_diagrams(new_diags, old_diags)[source]¶

Eliminate diagrams having a topologically equivalent diag.

Attibutes:: new_diags (list): The list of newly created PBMBPT diagrams. old_diags (list): The list of already checked PBMBPT diagrams.

adg.pbmbpt.generate_anomalous_diags(diag, nbody_max)[source]¶

Generate PBMBPT graphs with anomalous lines, with some redundancy.

Parameters:	diag (BmbptFeynmanDiagram) – The diagram to generate children from. nbody_max (int) – The maximal n-body character of a graph vertex.
Returns:	The anomalous graphs generated.
Return type:	(list)

adg.pbmbpt.generate_combinations(iter_list)[source]¶

Generate all possible combinations of length 1 to total.

adg.pbmbpt.iter_list¶

A list of iterable objects.

Type:	list

Returns:	A list with all the possible combinations of all lengths.
Return type:	(list)

>>> print(generate_combinations([1, 2, 3]))
[(1,), (1, 2), (1, 2, 3), (1, 3), (2,), (2, 3), (3,)]

adg.pbmbpt.unique_edge_combinations(edges, permutations)[source]¶

Return all edge combinations not producing equivalent anomalous graphs.

adg.pbmbpt.edges¶

The edges that can be modified.

Type:	list

adg.pbmbpt.permutations¶

The permutation generating equivalent diagrams.

Type:	list

Returns:	The list of edges producing unique anomalous diagrams.
Return type:	(list)

>>> edges = [(1, 3), (2, 3)]
>>> permutations = [{1: 1, 2: 2}, {1: 2, 2: 1}]
>>> print(unique_edge_combinations(edges, permutations))
[((1, 3), (2, 3)), ((2, 3),)]

adg.pbmbpt.unique_vertex_combinations(vertices, permutations)[source]¶

Return vertex combinations generating unique anomalous diagrams.

Return combinations of vertices on which self-contractions can be added without producing topologically equivalent PBMBPT diagrams.

adg.pbmbpt.vertices¶

Vertices that can be self-contracted.

Type:	list

adg.pbmbpt.permutations

The permutations that generate equivalent diags.

Type:	list

Returns:	Vertex combinations that do not produce equivalent diags.
Return type:	(list)

>>> vertices = [1, 3]
>>> permutations = [{1: 1, 3: 3}, {1: 3, 3: 1}]
>>> print(unique_vertex_combinations(vertices, permutations))
[(1, 3), (3,)]