{ }
View source on GitHub |
Construct the reduced Hamiltonian.
openfermion.chem.make_reduced_hamiltonian(
molecular_hamiltonian: openfermion.ops.InteractionOperator
,
n_electrons: int
) -> openfermion.ops.InteractionOperator
This Hamiltonian is equivalent to the electronic structure Hamiltonian but contains only two-body terms. To do this, the operator now depends on the number of particles being simulated. We use the RDM sum rule to lift the 1-body terms to the two-body space.
Derivation | |
---|---|
use the fact that i^l = (1/(n -1)) sum{jk}\delta{jk}i^ j^ k l
i^l = (-1/(n -1)) sum{jk}\delta{jk}j^ i^ k l
i^l = (-1/(n -1)) sum{jk}\delta{jk}i^ j^ l k
i^l = (1/(n -1)) sum{jk}\delta{jk}j^ i^ l k
Rewrite each one-body term as an even weighting of all four 2-RDM elements with delta functions. Then rearrange terms so that each ijkl term gets a sum of permuted one-body terms multiplied by delta function. One should notice that this results in the same formula if one was to apply the wedge product! |
Args | |
---|---|
molecular_hamiltonian
|
operator to write reduced hamiltonian for |
n_electrons
|
number of electrons in the system |
Returns | |
---|---|
InteractionOperator with a zero one-body component. |