openfermion.chem.make_reduced_hamiltonian
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.
|
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Last updated 2024-04-26 UTC.
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