fqe.diagonal_coulomb.DiagonalCoulomb

The diagonal coulomb Hamiltonian is characterized as being a two-body

Inherits From: Hamiltonian

fqe.diagonal_coulomb.DiagonalCoulomb(
    h2e: np.ndarray,
    e_0: complex = (0.0 + 0.0j)
) -> None

operator with a specific structure such that it is the product of two number operators. It is generally written as

.. math:: \hat{H} = E_0 + \sum_r f_r \hat{n}_r

    + \sum_{rs} v_{rs} \hat{n}_r \hat{n}_s

where n is a number operator. Note that this Hamiltonian is diagonal in the Slater determinant space,

.. math:: \langle I|\hat{H}|J\rangle = pI \delta{IJ}

where p is an appropriate factor.

h2e either (1) a dense rank-2 array that contains the diagonal elements :math:|v_{rs}| above, or (2) a dense rank-4 array in the format used for two-body operator in the dense Hamiltonian code.
e_0 Scalar potential associated with the Hamiltonian.

Methods

calc_diag_transform

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calc_diag_transform() -> np.ndarray

Performs a unitary digaonlizing transformation of the one-body term and returns that transformation.

conserve_number

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conserve_number() -> bool

Returns True if the Hamiltonian is number conserving, else False.

diag_values

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diag_values() -> np.ndarray

Returns the diagonal values packed into a single dimension.

diagonal

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diagonal() -> bool

Returns True if the Hamiltonian is diagonal, else False.

diagonal_coulomb

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diagonal_coulomb() -> bool

Returns whether or not the Hamiltonian is diagonal_coulomb.

dim

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dim() -> int

Returns is the orbital dimension of the Hamiltonian arrays.

e_0

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e_0()

Returns the scalar potential of the Hamiltonian.

iht

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iht(
    time: float
)

Returns the matrices of the Hamiltonian prepared for time evolution.

Args
time The time step.

quadratic

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quadratic() -> bool

Returns True if the Hamiltonian is quadratic, else False.

rank

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rank() -> int

Returns the rank of the largest tensor.

tensors

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tensors() -> Tuple[np.ndarray, ...]

Returns all tensors in order of their rank.

transform

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transform(
    trans: np.ndarray
) -> np.ndarray

Tranform the one body term using the provided matrix.

Args
trans Unitary transformation.

Returns
Transformed one-body Hamiltonian as a numpy.ndarray.