# What is the meaning of k,l,m,n in this second quantized hamiltonian?

The following is a screenshot from chapter 8, by Wouters et al, titled "Five Years of Density Matrix Embedding Theory", in the book "Fragmentation: Toward Accurate Calculations on Complex Molecular Systems":

What do the indices k,l,m,n in the equation $$H=E_{nuc}+\sum{t_{kl}a_{kl}^\dagger a_{kl}}+\frac1 2 \sum{(kl|mn)a_{k}^\dagger a_m^\dagger a_n a_l}$$ stand for?

This equation appears in a paper on density matrix embedding theory(DMET). I understand that creation and annihilation operations are used but have no clue about the indices jklm.

Also, how do I interpret the given hamiltonian?

I think they might have something to do with spin orbitals or two-electron integrals. The paper itself does not give much context for the equation.

• You might want to have this question migrated to the matter modeling SE site. Jul 30 at 9:13