Add support for non-sorted and overlapping indices in MPOHamiltonian constructors

[lkdvos]

No description provided.

[codecov]

Codecov Report

❌ Patch coverage is 92.50000% with 3 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/operators/mpo.jl	83.33%	3 Missing ⚠️

Files with missing lines	Coverage Δ
src/operators/mpohamiltonian.jl	89.90% <100.00%> (+0.36%)	⬆️
src/operators/mpo.jl	87.21% <83.33%> (-0.35%)	⬇️

... and 2 files with indirect coverage changes

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[VictorVanthilt]

Could you give some insight as to why we need to swap and multiply neighbours?

[lkdvos]

The obvious case is an exchange integral (ie for quantum chemistry)

T = rand(N, N) # kinetic
V = rand(N, N, N, N) # exchange
H = FiniteMPOHamiltonian(fill(V, N), (i, j) => T[i, j] * c_min() \otimes c_plus()) +
    FiniteMPOHamiltonian(fill(V, N), (i, j, k, l) => V[i, j, k, l] * c_min() \otimes c_min() \otimes c_plus() \otimes c_plus())

[VictorVanthilt]

But $X\otimes X \otimes Y \otimes Y$ applied on sites 1, 1, 1 and 1 just sits wrong with me. The operator lives on a 4-site Hilbertspace but it acts on only the first one?

[lkdvos]

Does it help if you rewrite this as $H = \sum_{ijkl} V_{ijkl} c_i c_j c^\dagger_k c^\dagger_l$?