BIMSRG Diagram

Routines and class for Bogoliubov IMSRG diagrams.

class adg.bimsrg.BimsrgDiagram(nx_graph, tag_num)

Bases: adg.diag.Diagram

Describes a B-IMSRG Feynman diagram with its related properties.

adjacency_mat

The adjacency matrix of the diagram.

Type:Numpy array

unique_id

A unique number associated to the diagram.

Type:int

expr

The B-IMSRG expression associated to the diagram.

Type:str

ext_io_degree

The degree of the operator component the diagram corresponds to.

Type:tuple

is_AB

True if the diagram contributes to +AB, false if to -BA.

Type:bool

adjacency_mat

attribute_expression()

Returns the LaTeX expression of the diagram.

The expression is extracted in a way that assumes the canonical representation of the vertices as well as a labeling of the external lines that would correspond to a canonical representation of the C operator vertex. As such, there is no sign factor associated to departing from the canonical representation of the diagram. This additionally prevents any line crossing from appearing.

Returns:The LaTeX expression for the diagram. Return type:(str)

degrees

expr

ext_io_degree

graph

io_degrees

is_AB

max_degree

permutator()

Return the permutator associated to the diagram.

The labelling of the external lines correspond to the canonical representation of the C operator vertex.

Returns:The permutator associated to the diagram in LaTeX format. Return type:(str)

sign()

Return the sign of the diagram.

As the diagrams are made with vertices in canonical representation and avoiding crossings, the only sign left is associated with the commutator.

Returns:The sign of the diagram. Return type:(str)

symmetry_factor()

Returns the symmetry factor of the diagram in LaTeX format.

Returns:The LaTeX-formatted symmetry factor. Return type:(str)

tags

unique_id

unsort_degrees

unsort_io_degrees

vertices_expression()

Return the expression associated to the vertices in LaTeX format.

The expressions are extracted in a way that assumes the canonical representation of the vertices as well as a labeling of the external lines that would correspond to a canonical representation of the C operator vertex. This prevents any crossing as well as additional sign tied to departing from the canonical representation.

Returns:The LaTeX-formatted expression for the vertices. Return type:(str)

write_graph(latex_file, directory, write_time)

Write the graph of the diagram to the LaTeX file.

Parameters:

• latex_file (file) – The LaTeX ouput file of the program.
• directory (str) – Path to the result folder.
• write_time (bool) – (Here to emulate polymorphism).

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.

adg.bimsrg.diagrams_generation(orders)

Generate diagrams for B-IMSRG.

Parameters:orders (tuple) – The B-IMSRG (N_A, N_B, N_C) order of the diagrams. Returns:

NumPy arrays encoding the adjacency matrices of the graphs,

and number of diagrams with the A vertex on top.

Return type:(tuple)

adg.bimsrg.diagrams_subset(deg_max_top, deg_max_bot, deg_max_ext)

Generate diagrams for B-IMSRG.

Parameters:orders (tuple) – The max ranks (2*N_A, 2*N_B, 2*N_C) of the vertices. Returns:NumPy arrays encoding the adjacency matrices of the graphs. Return type:(list)

>>> diagrams_subset(2, 2, 0) # doctest: +NORMALIZE_WHITESPACE
[array([[0, 0, 0, 0],
       [0, 0, 2, 0],
       [0, 0, 0, 0],
       [0, 0, 0, 0]])]
>>> len(diagrams_subset(2, 2, 2))
5
>>> len(diagrams_subset(4, 4, 4))
41
>>> len(diagrams_subset(0, 0, 0))
0

adg.bimsrg.order_diagrams(diagrams, order)

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

Parameters:

• diagrams (list) – The unordered BimsrgDiagrams.
• order (int) – The order of the B-IMSRG truncation.

Returns:

First element are the ordered BimsrgDiagrams. Second element is the number of diagrams for each type. Third element is flags for the output processing.

Return type:

(tuple)

adg.bimsrg.permutator(set_1, set_2)

Write the definition of the permutation operator given by the two sets.

Parameters:

• set_1 (list) – The list of the left-hand-side qp labels.
• set_2 (list) – The list of the right-hand-side qp labels.

Returns:

The LaTeX expression for the permutation operator.

Return type:

(str)

>>> print(permutator([1, 2], [3])) # doctest: +NORMALIZE_WHITESPACE
P(k_{1}k_{2}/k_{3}) &= 1 - P_{k_{1} k_{3}} - P_{k_{2} k_{3}} \\

adg.bimsrg.two_partitions(number)

Return 2-partitions of the given integer.

Parameters:numbr (int) – The integer to partition. Returns:All the 2-partitions as tuples. Return type:(list)

>>> two_partitions(3)
[(0, 3), (1, 2), (2, 1), (3, 0)]

>>> two_partitions(0)
[(0, 0)]

>>> two_partitions(-1)
[]

adg.bimsrg.write_header(tex_file, commands, diags_nbs)

Write overall header for BIMSRG 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.

adg.bimsrg.write_permutator_section(tex_file, commands)

Write the section defining permutation operators.

Parameters:

• tex_file (file) – The ouput LaTeX file of the program.
• commands (Namespace) – Flags for the program run.