RealOperator4DTensor

Represents a 4D tensor operator, such as CoulombSum or PairHopSum.

Factories

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.

PairHopSum(const RealTensor tensor) -> RealOperator4DTensor

Returns a generalized pair hopping tensor operator $\sum_{i,j,k,l} V_{ijkl} a_{i}^\dagger a_{j}^\dagger a_{k} a_{l}$.

The operator is parametrized by a 4-rank tensor $V_{ijkl}$ with $L^4$ elements. It acts directly according to the provided index positions, mapping exactly 1-to-1 with the underlying $L$ qubit sites.

Note the difference to CoulombSum: PairHopSum does not make any assumptions about interleaved spin mappings. The operator natively preserves particle number.

Parameters

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