ffsim.random.random_double_factorized_hamiltonian

ffsim.random.random_double_factorized_hamiltonian(norb, *, rank=None, z_representation=False, real=False, seed=None)[source]

Sample a random double-factorized Hamiltonian.

The two-body part of the Hamiltonian is a sum of rank terms, each built from an independent random orbital rotation and an independent random diagonal Coulomb matrix sampled from the Gaussian orthogonal ensemble (see random_real_symmetric_matrix()). The diagonal Coulomb matrices are divided by the square root of the rank so that the scale of the two-body part does not depend on the rank: the terms are independent and have mean zero, so their sum fluctuates on the scale of the square root of the number of terms.

Parameters:

  • norb (int) – The number of spatial orbitals.

  • rank (int | None) – The desired number of terms in the two-body part of the Hamiltonian. If not specified, it will be set to norb * (norb + 1) // 2.

  • z_representation (bool) – Whether to return a Hamiltonian in the “Z” representation.

  • real (bool) – Whether to sample a real-valued object rather than a complex-valued one.

  • seed – A seed to initialize the pseudorandom number generator. Should be a valid input to np.random.default_rng.

Return type:

DoubleFactorizedHamiltonian

Returns:

The sampled double-factorized Hamiltonian.