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1.15.0
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TRIQS/TRIQS 4.0.0
Researching Interacting Quantum Systems
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#include <triqs/hilbert_space/fundamental_operator_set.hpp>
Class representing a fundamental operator set.
A fundamental operator set is an ordered set of single particle state indices, \( A = \{ \alpha_i \}_{i=0}^{N-1} \), where the corresponding states \( \{ \lvert \alpha_i \rangle \}_{i=0}^{N-1} \) span a 1-particle Hilbert space \( \mathcal{H}_1 \) of finite dimension \( N \). By ordered, we mean that there is a strict total order imposed on the set \( A \) such that \( \alpha_i < \alpha_j \) if \( i < j \).
Each index \( \alpha_i \) can consist of an arbitrarily long sequence of integers, strings, doubles and arrays of integers. We write \( \alpha_i = (\beta^{(i)}_1, \dots, \beta^{(i)}_{k_i}) \), where each \( \beta^{(i)}_j \) is either an integer, a string, a double or an array of integers.
For example, fermionic operators are often characterized by a spin index \( \sigma \) and an orbital index \( a \) such that \( \alpha = (\sigma, a) \). Considering fermions with spins \( \sigma \in \{ \text{"up"}, \text{"down"} \} \) and 3 orbitals \( a \in \{ 0, 1, 2 \} \), the fundamental operator set is given by
\[ A = \{ (\text{"up"}, 0), (\text{"up"}, 1), (\text{"up"}, 2), (\text{"down"}, 0), (\text{"down"}, 1), (\text{"down"}, 2) \} \; . \]
Definition at line 94 of file fundamental_operator_set.hpp.
Public Types | |
| using | const_iterator = triqs::utility::dressed_iterator<_enum_iterator, _cdress> |
| Constant iterator type. | |
| using | data_t = std::vector<indices_t> |
| Container type to store \( A = \{ \alpha_i \}_{i=0}^{N-1} \). | |
| using | indices_t = triqs::hilbert_space::indices_t |
| Index type to represent a single \( \alpha_i \). | |
Public Member Functions | |
| fundamental_operator_set ()=default | |
| Default constructor leaves the set of indices empty, i.e. \( A = \emptyset \). | |
| fundamental_operator_set (data_t v) | |
| Construct a fundamental operator set from a vector of indices \( \mathbf{v} = (\alpha_0, \dots,
\alpha_{N-1}) \). | |
| fundamental_operator_set (gf_struct_t const &gf_struct) | |
| Construct a fundamental operator set from a triqs::gfs::gf_struct_t object. | |
| template<typename IndexType> | |
| fundamental_operator_set (std::set< IndexType > const &A) | |
| Construct a fundamental operator set from a set of indices \( A = \{ \alpha_0, \dots, \alpha_{N-1} \}
\). | |
| fundamental_operator_set (std::vector< int > const &v) | |
| Construct a fundamental operator set from a vector of integers \( \mathbf{v} = (v_1, \dots, v_k) \). | |
| const_iterator | begin () const noexcept |
| Get a const iterator to the beginning of the set. | |
| const_iterator | cbegin () const noexcept |
| Get a const iterator to the beginning of the set. | |
| auto | cend () const noexcept |
| Get a const iterator to the end of the set. | |
| data_t const & | data () const |
| Get the ordered set \( A = \{ \alpha_i \}_{i=0}^{N-1} \). | |
| auto | end () const noexcept |
| Get a const iterator to the end of the set. | |
| bool | has_indices (indices_t const &alpha) const |
| Check if a given \( \alpha \) is in the set. | |
| template<typename... Bs> | |
| void | insert (Bs const &...betas) |
| Insert a new index \( \alpha = (\beta_1, \dots, \beta_k) \) into the set. | |
| void | insert_from_indices_t (indices_t const &alpha) |
| Insert a new index \( \alpha \) into the set. | |
| operator data_t () const | |
| Explicit conversion operator to a std::vector of indices_t. | |
| bool | operator== (fundamental_operator_set const &fops) const |
| Equal-to operator compares the ordered sets of indices for equality. | |
| auto | operator[] (indices_t const &alpha) const |
| Subscript operator to get the position of a given index \( \alpha \) in the set. | |
| auto | size () const |
| Get the number \( N \) of single particle state indices in the set. | |
Friends | |
| void | h5_read_attribute (h5::object obj, std::string const &name, fundamental_operator_set &fops) |
| Read a triqs::hilbert_space::fundamental_operator_set from an HDF5 attribute. | |
| void | h5_write_attribute (h5::object obj, std::string const &name, fundamental_operator_set const &fops) |
| Write a triqs::hilbert_space::fundamental_operator_set to HDF5 as an attribute. | |
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inline |
Construct a fundamental operator set from a vector of integers \( \mathbf{v} = (v_1, \dots, v_k) \).
The set will contain indices \( \alpha_i = (\beta^{(i)}_1, \beta^{(i)}_2) \) with \( \beta^{(i)}_1 \in \{ 0, \dots, k-1 \} \) and \( \beta^{(i)}_2 \in \{ 0, \dots, v_{\beta^{(i)}_1} \} \).
For example, given \( \mathbf{v} = (2, 1, 3) \), the generated fundamental operator set is
\[ A = \{ (0, 0), (0, 1), (1, 0), (2, 0), (2, 1), (2, 2) \} \; . \]
| v | Vector of integers \( \mathbf{v} \). |
Definition at line 123 of file fundamental_operator_set.hpp.
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inline |
Construct a fundamental operator set from a set of indices \( A = \{ \alpha_0, \dots, \alpha_{N-1} \} \).
| IndexType | Index type. |
| A | Set of indices \( A \). |
Definition at line 137 of file fundamental_operator_set.hpp.
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inlineexplicit |
Construct a fundamental operator set from a vector of indices \( \mathbf{v} = (\alpha_0, \dots, \alpha_{N-1}) \).
| v | Vector of indices \( \mathbf{v} \). |
Definition at line 149 of file fundamental_operator_set.hpp.
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inline |
Construct a fundamental operator set from a triqs::gfs::gf_struct_t object.
A triqs::gfs::gf_struct_t object determines the shape of a block Green's function. It is a vector of pairs, where each pair consists of a block name \( s \) and block size \( b_s \). The size of the vector \(k \) corresponds to the number of blocks.
The set will contain indices \( \alpha_i = (\beta^{(i)}_1, \beta^{(i)}_2) \) with \( \beta^{(i)}_1 \in \{ s_1, \dots, s_k \} \) and \( \beta^{(i)}_2 \in \{ 0, \dots, b_{\beta^{(i)}_1} - 1 \} \).
For example, given the block structure \(\left( (\text{"up"}, 2), (\text{"down"}, 3) \right) \), the generated fundamental operator set is
\[ A = \{ (\text{"up"}, 0), (\text{"up"}, 1), (\text{"down"}, 0), (\text{"down"}, 1), (\text{"down"}, 2) \} \; . \]
| gf_struct | A triqs::gfs::gf_struct_t object representing the structure of a Green's function. |
Definition at line 169 of file fundamental_operator_set.hpp.
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inlinenodiscard |
Check if a given \( \alpha \) is in the set.
| alpha | Index \( \alpha \) to look up. |
Definition at line 211 of file fundamental_operator_set.hpp.
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inline |
Insert a new index \( \alpha = (\beta_1, \dots, \beta_k) \) into the set.
It calls insert_from_indices_t() with the index \( \alpha \) constructed from the given \( \beta_i \).
| Bs | Types of \( \beta_i \). |
| betas | \( \beta_1, \dots, \beta_k \) that form the index \( \alpha \). |
Definition at line 200 of file fundamental_operator_set.hpp.
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inline |
Insert a new index \( \alpha \) into the set.
The index is inserted at end of the set such that \( \alpha_i < \alpha \) for all existing indices \(\alpha_i \) in the set.
It does nothing if the index is already present.
| alpha | Index \( \alpha \) to insert. |
Definition at line 187 of file fundamental_operator_set.hpp.
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inlinenodiscard |
Subscript operator to get the position of a given index \( \alpha \) in the set.
It throws an exception if \( \alpha \notin A \).
| alpha | Index \( \alpha \) to look up. |
Definition at line 221 of file fundamental_operator_set.hpp.
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friend |
Read a triqs::hilbert_space::fundamental_operator_set from an HDF5 attribute.
| obj | h5::object the attribute belongs to. |
| name | Name of the attribute. |
| fops | Fundamental operator set to be read into. |
Definition at line 126 of file fundamental_operator_set.cpp.
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friend |
Write a triqs::hilbert_space::fundamental_operator_set to HDF5 as an attribute.
| obj | h5::object the attribute belongs to. |
| name | Name of the attribute. |
| fops | Fundamental operator set to be written. |
Definition at line 122 of file fundamental_operator_set.cpp.
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