dyson.expressions.hamiltonian

Hamiltonian-driven expressions.

Classes

Hamiltonian(hamiltonian[, bra, ket])

Hamiltonian-driven expressions for the Green's function.

class dyson.expressions.hamiltonian.Hamiltonian(hamiltonian: Array | SparseArray, bra: Array | None = None, ket: Array | None = None)

Bases: BaseExpression

Hamiltonian-driven expressions for the Green’s function.

classmethod from_mf(mf: RHF) → Hamiltonian

Create an expression from a mean-field object.

Parameters:

mf – Mean-field object.

Returns:

Expression object.

apply_hamiltonian(vector: Array) → Array

Apply the Hamiltonian to a vector.

Parameters:

vector – Vector to apply Hamiltonian to.

Returns:

Output vector.

apply_hamiltonian_left(vector: Array) → Array

Apply the Hamiltonian to a vector on the left.

Parameters:

vector – Vector to apply Hamiltonian to.

Returns:

Output vector.

diagonal() → Array

Get the diagonal of the Hamiltonian.

Returns:

Diagonal of the Hamiltonian.

build_matrix() → Array

Build the Hamiltonian matrix.

Returns:

Hamiltonian matrix.

get_excitation_bra(orbital: int) → Array

Obtain the bra vector corresponding to a fermionic operator acting on the ground state.

The bra vector is the excitation vector corresponding to the bra state, which may or may not be the same as the ket state vector.

Parameters:

orbital – Orbital index.

Returns:

Bra excitation vector.

See also

get_excitation_vector(): Function to get the excitation vector when the bra and ket are the same.

get_excitation_ket(orbital: int) → Array

Obtain the vector corresponding to a fermionic operator acting on the ground state.

This vector is a generalisation of

\[f_i^{\pm} \left| \Psi_0 \right>\]

where \(f_i^{\pm}\) is the fermionic creation or annihilation operator, or a product thereof, depending on the particular expression and what Green’s function it corresponds to.

The vector defines the excitaiton manifold probed by the Green’s function corresponding to the expression.

Parameters:

orbital – Orbital index.

Returns:

Excitation vector.

get_excitation_vector(orbital: int) → Array

Obtain the vector corresponding to a fermionic operator acting on the ground state.

This vector is a generalisation of

\[f_i^{\pm} \left| \Psi_0 \right>\]

where \(f_i^{\pm}\) is the fermionic creation or annihilation operator, or a product thereof, depending on the particular expression and what Green’s function it corresponds to.

The vector defines the excitaiton manifold probed by the Green’s function corresponding to the expression.

Parameters:

orbital – Orbital index.

Returns:

Excitation vector.

build_se_moments(nmom: int, reduction: Reduction = Reduction.NONE) → Array

Build the self-energy moments.

Parameters:

• nmom – Number of moments to compute.

• reduction – Reduction method to apply to the moments.

Returns:

Moments of the self-energy.

property mol: Mole

Molecule object.

property non_dyson: bool

Whether the expression produces a non-Dyson Green’s function.

property nphys: int

Number of physical orbitals.

property nsingle: int

Number of configurations in the singles sector.

property nconfig: int

Number of configurations in the non-singles sectors.

property shape: tuple[int, int]

Shape of the Hamiltonian matrix.

property nocc: int

Number of occupied orbitals.

property nvir: int

Number of virtual orbitals.