CoulombSum

Overloads

Name	Description
CoulombSum(const RealTensor tensor) -> RealOperator4DTensor	Returns a Coulomb tensor operator sum $\sum_{i,j,k,l,\sigma,\sigma'} V_{ijkl} a_{i\sigma}^\dagger a_{j\sigma'}^\dagger a_{k\sigma'} a_{l\sigma}$.
CoulombSum(const ComplexTensor tensor) -> ComplexOperator4DTensor	Returns a Coulomb tensor operator sum $\sum_{i,j,k,l,\sigma,\sigma'} V_{ijkl} a_{i\sigma}^\dagger a_{j\sigma'}^\dagger a_{k\sigma'} a_{l\sigma}$.

CoulombSum(const RealTensor tensor) -> RealOperator4DTensor

Returns a Coulomb tensor operator sum $\sum_{i,j,k,l,\sigma,\sigma'} V_{ijkl} a_{i\sigma}^\dagger a_{j\sigma'}^\dagger a_{k\sigma'} a_{l\sigma}$.

The operator is parametrized by a 4-rank tensor $V_{ijkl}$ with $(L/2)^4$ elements. It acts on a $2^{L}$-dimensional Hilbert space assuming interleaved spins, where spatial orbital $i$ corresponds to spin-up position $2i$ and spin-down position $2i+1$.

Note the difference to PairHopSum: CoulombSum assumes implicit physical spin degrees of freedom. Spatial orbital indices up to $L/2$ implicitly expand to cover $L$ qubit sites.

Parameters

• tensor: The 4-rank tensor $V_{ijkl}$ representing the interaction.

CoulombSum(const ComplexTensor tensor) -> ComplexOperator4DTensor

Returns a Coulomb tensor operator sum $\sum_{i,j,k,l,\sigma,\sigma'} V_{ijkl} a_{i\sigma}^\dagger a_{j\sigma'}^\dagger a_{k\sigma'} a_{l\sigma}$.

The operator is parametrized by a 4-rank tensor $V_{ijkl}$ with $(L/2)^4$ elements. It acts on a $2^{L}$-dimensional Hilbert space assuming interleaved spins, where spatial orbital $i$ corresponds to spin-up position $2i$ and spin-down position $2i+1$.

Note the difference to PairHopSum: CoulombSum assumes implicit physical spin degrees of freedom. Spatial orbital indices up to $L/2$ implicitly expand to cover $L$ qubit sites.

Parameters

• tensor: The 4-rank tensor $V_{ijkl}$ representing the interaction.