ffsim.rdms

ffsim.rdms(vec, norb, nelec, *, rank=1, spin_summed=False, reorder=True)[source]

Return the reduced density matrices of a state vector.

The rank 1 RDM is defined as follows:

rdm1[p, q] = ⟨p+ q⟩

The definition of higher-rank RDMs depends on the reorder argument, which defaults to True.

reorder = True

The reordered RDMs are defined as follows:

rdm2[p, q, r, s] = ⟨p+ r+ s q⟩
rdm3[p, q, r, s, t, u] = ⟨p+ r+ t+ u s q⟩
rdm4[p, q, r, s, t, u, v, w] = ⟨p+ r+ t+ v+ w u s q⟩

reorder = False

If reorder is set to False, the RDMs are defined as follows:

rdm2[p, q, r, s] = ⟨p+ q r+ s⟩
rdm3[p, q, r, s, t, u] = ⟨p+ q r+ s t+ u⟩
rdm4[p, q, r, s, t, u, v, w] = ⟨p+ q r+ s t+ u v+ w⟩

Note

Currently, only ranks 1 and 2 are supported.

Parameters:

  • vec (ndarray) – The state vector whose reduced density matrix is desired.

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

  • nelec (tuple[int, int]) – The number of alpha and beta electrons.

  • rank (int) – The rank of the reduced density matrix.

  • spin_summed (bool) – Whether to return the “spin-summed” RDMs.

  • reorder (bool) – Whether to reorder the indices of the reduced density matrix.

Return type:

ndarray | tuple[ndarray, ...]

Returns:

The reduced density matrices. All RDMs up to and including the specified rank are returned, in increasing order of rank. For example, if rank=2 then a tuple (rdm1, rdm2) is returned. The 1-RDMs are: (alpha-alpha, beta-beta). The spin-summed 1-RDM is alpha-alpha + alpha-beta. The 2-RDMs are: (alpha-alpha, alpha-beta, beta-beta). The spin-summed 2-RDM is alpha-alpha + alpha-beta + beta-alpha + beta-beta.