ffsim.apply_quad_ham_evolution

ffsim.apply_quad_ham_evolution(vec, mat, time, norb, nelec, *, copy=True)[source]

Apply time evolution by a quadratic Hamiltonian.

Applies

\[\begin{split}\exp\left(-i t \sum_{\substack{ij \\ \sigma}} \mathbf{M}^{(\sigma)}_{ij} a^\dagger_{i\sigma} a_{j\sigma}\right)\end{split}\]

where each \(\mathbf{M}^{(\sigma)}\) is a Hermitian matrix.

Parameters:

  • vec (ndarray) – The state vector to be transformed.

  • mat (ndarray | tuple[ndarray | None, ndarray | None]) – The matrix \(\mathbf{M}\) describing the quadratic Hamiltonian. You can pass either a single Numpy array specifying the Hamiltonian to use for both spin sectors, or you can pass a pair of Numpy arrays specifying independent Hamiltonians for spin alpha and spin beta. If passing a pair, you can use None for one of the values in the pair to indicate that no operation should be applied to that spin sector.

  • time (float) – The evolution time.

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

  • nelec (int | tuple[int, int]) – Either a single integer representing the number of fermions for a spinless system, or a pair of integers storing the numbers of spin alpha and spin beta fermions.

  • copy (bool) –

    Whether to copy the vector before operating on it.

    • If copy=True then this function always returns a newly allocated vector and the original vector is left untouched.

    • If copy=False then this function may still return a newly allocated vector, but the original vector may have its data overwritten. It is also possible that the original vector is returned, modified in-place.

Return type:

ndarray

Returns:

The evolved state vector.