triqs::hilbert_space::hilbert_space

#include <triqs/hilbert_space/hilbert_space.hpp>

Detailed Description

Fermionic Hilbert (Fock) space generated by a fundamental operator set.

The Hilbert (Fock) space \( \mathcal{F} \) is fully defined by its underlying fundamental operator set \( A = \{ \alpha_i \}_{i=0}^{N-1} \) (see triqs::hilbert_space::fundamental_operator_set). Its dimension is \(\dim(\mathcal{F}) = 2^N \).

As explained in Operators, we can map each occupation number basis state \( \lvert n_{\alpha_0}, n_{\alpha_1}, \dots, n_{\alpha_{N-1}} \rangle = \lvert f \rangle \in \mathcal{F} \) to an integer \( f \in \{ 0, \dots, 2^N - 1 \} \) and back. This allows us to write the complete set of basis states of \( \mathcal{F} \) as \( B_{\mathcal{F}} = \{ \lvert f \rangle \}_{f=0}^{2^N - 1} \). Furthermore, it imposes a natural order on \(B_{\mathcal{F}} \) such that \( \lvert f \rangle < \lvert f' \rangle \) if \( f < f' \).

Note

This class is a minimal implementation of a Hilbert space. It only stores its dimension and relies completely on the encoding of occupation number basis states as integers.

Definition at line 71 of file hilbert_space.hpp.

Public Member Functions
	hilbert_space ()
	Default constructor constructs an empty Hilbert (Fock) space of dimension \( 0 \).
	hilbert_space (fundamental_operator_set const &fops)
	Construct a Hilbert (Fock) space from a given triqs::hilbert_space::fundamental_operator_set object.
fock_state_t	get_fock_state (fundamental_operator_set const &fops, std::set< fundamental_operator_set::indices_t > const &alphas) const
	Get the Fock state \( \lvert f \rangle = \prod_{j=1}^k \hat{c}^\dagger_{\alpha_{i_j}} \lvert 0 \rangle \).
fock_state_t	get_fock_state (int f) const
	Get the Fock state \( \lvert f \rangle \) corresponding to a given integer \( f \).
auto	get_state_index (fock_state_t f) const
	Get the integer \( f \) corresponding to a given Fock state \( \lvert f \rangle \).
bool	has_state (fock_state_t f) const
	Check if a given Fock state belongs to the Hilbert (Fock) space.
bool	operator== (hilbert_space const &hs) const
	Equal-to operator compares the dimensions of the two Hilbert (Fock) spaces.
auto	size () const
	Get the dimension \( \dim(\mathcal{F}) \) of the Hilbert (Fock) space \( \mathcal{F} \).

Static Public Member Functions
static std::string	hdf5_format ()
	Get the HDF5 format tag.

Friends
void	h5_read (h5::group g, std::string const &name, hilbert_space &hs)
	Read a triqs::hilbert_space::hilbert_space from HDF5.
void	h5_write (h5::group g, std::string const &name, hilbert_space const &hs)
	Write a triqs::hilbert_space::hilbert_space to HDF5.

Constructor & Destructor Documentation

hilbert_space()

triqs::hilbert_space::hilbert_space::hilbert_space ( fundamental_operator_set const & fops )

inline

Construct a Hilbert (Fock) space from a given triqs::hilbert_space::fundamental_operator_set object.

If the size of the fundamental operator set is \( N \), then the dimension of the constructed Hilbert (Fock) space is \( \dim(\mathcal{F}) = 2^N \).

Parameters

fops	Fundamental operator set that generates the Hilbert (Fock) space.

Definition at line 84 of file hilbert_space.hpp.

Member Function Documentation

get_fock_state() [1/2]

fock_state_t triqs::hilbert_space::hilbert_space::get_fock_state ( fundamental_operator_set const & fops, std::set< fundamental_operator_set::indices_t > const & alphas ) const

inlinenodiscard

Get the Fock state \( \lvert f \rangle = \prod_{j=1}^k \hat{c}^\dagger_{\alpha_{i_j}} \lvert 0 \rangle \).

Parameters

fops	triqs::hilbert_space::fundamental_operator_set object that defines the Hilbert (Fock) space \(\mathcal{F} \).
alphas	Set of indices \( \{ \alpha_{i_1}, \dots, \alpha_{i_k} \} \) specifying the creation operators.

Returns

Fock state \( \lvert f \rangle \).

Definition at line 136 of file hilbert_space.hpp.

get_fock_state() [2/2]

fock_state_t triqs::hilbert_space::hilbert_space::get_fock_state ( int f ) const

inlinenodiscard

Get the Fock state \( \lvert f \rangle \) corresponding to a given integer \( f \).

It throws an exception if \( f \geq 2^N = \dim{\mathcal{F}} \).

Parameters

f	Integer \( f \) representing the Fock state \( \lvert f \rangle \).

Returns

Fock state \( \lvert f \rangle \).

Definition at line 122 of file hilbert_space.hpp.

get_state_index()

auto triqs::hilbert_space::hilbert_space::get_state_index ( fock_state_t f ) const

inlinenodiscard

Get the integer \( f \) corresponding to a given Fock state \( \lvert f \rangle \).

It throws an exception if the given Fock state is not in the Hilbert (Fock) space, i.e. if \( f \geq 2^N = \dim{\mathcal{F}} \).

Parameters

f	Fock state \( \lvert f \rangle \).

Returns

Integer \( f \).

Definition at line 109 of file hilbert_space.hpp.

has_state()

bool triqs::hilbert_space::hilbert_space::has_state ( fock_state_t f ) const

inlinenodiscard

Check if a given Fock state belongs to the Hilbert (Fock) space.

Parameters

f	Fock state \( \lvert f \rangle \).

Returns

True if \( f < 2^N = \dim{\mathcal{F}} \), false otherwise.

Definition at line 98 of file hilbert_space.hpp.

Friends And Related Symbol Documentation

h5_read

void h5_read ( h5::group g, std::string const & name, hilbert_space & hs )

friend

Read a triqs::hilbert_space::hilbert_space from HDF5.

Parameters

g	h5::group to be read from.
name	Name of the subgroup.
hs	Hilbert (Fock) space to be read into.

Definition at line 165 of file hilbert_space.hpp.

h5_write

void h5_write ( h5::group g, std::string const & name, hilbert_space const & hs )

friend

Write a triqs::hilbert_space::hilbert_space to HDF5.

Parameters

g	h5::group to be written to.
name	Name of the subgroup.
hs	Hilbert (Fock) space to be written.

Definition at line 153 of file hilbert_space.hpp.

---

The documentation for this class was generated from the following file:

• triqs/hilbert_space/hilbert_space.hpp