read_representation

Reads an Representation object from a TOML file.

Sources read.hpp, read.cpp

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Definition

C++Julia

OpSum read_representation(FileToml file, std::string irrep_tag, 
                          std::string group_tag = "Symmetries");

read_representation(file::FileToml, irrep_tag::String, 
                    group_tag::String = "Symmetries")::Representation

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Parameters

Name	Description
file	FileToml object from which the Representation is read
irrep_tag	tag which holds the information about the Representation in the TOML file
group_tag	tag which holds the information about the PermutationGroup in the TOML file	"Symmetries"

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Data format

A Representation can be defined in a TOML file by specifying up two or three things:

1. The PermutationGroup as an integer matrix
2. The characters of the representation
3. (optional) the allowed_symmetries of the representation, i.e. a list of the number of symmetries used in the irrep. By default all symmetries of the group are used in the representation.

A typical specification of several Representations is shown here:

    Symmetries = [
      [0, 1, 2, 3],
      [1, 2, 3, 0],
      [2, 3, 0, 1],
      [3, 0, 1, 2]
    ]

    # real irrep, momentum 0
    [k_0]
    characters=[1.0, 1.0, 1.0, 1.0]

    # complex irrep, momentum pi/2
    [k_pi2]
    characters=[
      [1.0, 0.0], 
      [0.0, 1.0], 
      [-1.0, 0.0],
      [0.0, -1.0]
    ]

    # real irrep, momentum pi
    [k_pi]
    characters=[1.0, -1.0, 1.0, -1.0]

    # real irrep on subgroup
    [k_pi2_half]
    characters=[1.0, -1.0]
    allowed_symmetries=[0, 2]

1-indexing in Julia / 0-indexing in C++

To enumerate the sites of a Permutation, we start counting at 1 in Julia and 0 in C++.

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Usage Example

The example reads the representation defined in the irreps.toml file, whose contents are shown up in the section Data format.

C++Julia

std::string file = XDIAG_DIRECTORY "/misc/data/irreps.toml";
auto fl = FileToml(file);

auto k_0 = read_representation(fl, "k_0");
XDIAG_SHOW(k_0);
XDIAG_SHOW(isreal(k_0));

auto k_pi2 = read_representation(fl, "k_pi2");
XDIAG_SHOW(k_pi2);
XDIAG_SHOW(isreal(k_pi2));

auto k_pi = read_representation(fl, "k_pi");
XDIAG_SHOW(k_pi);
XDIAG_SHOW(isreal(k_pi));

auto k_pi2_half = read_representation(fl, "k_pi2_half");
XDIAG_SHOW(k_pi2_half);
XDIAG_SHOW(isreal(k_pi2_half));

file = "irreps.toml"
fl = FileToml(file)

k_0 = read_representation(fl, "k_0")
@show k_0
@show isreal(k_0)

k_pi2 = read_representation(fl, "k_pi2")
@show k_pi2
@show isreal(k_pi2)

k_pi = read_representation(fl, "k_pi")
@show k_pi
@show isreal(k_pi)

k_pi2_half = read_representation(fl, "k_pi2_half")
@show k_pi2_half
@show isreal(k_pi2_half)