[Feature Request] `expectation_value` for `VUMPS`

[sanderdemeyer]

Currently, we can calculate the expectation_value of a state, a LocalOperator, and a CTMRGEnv. It would be useful to also support something like expectation_value(state, O, (mps,env)), where mps (with its corresponding env) is the boundary MPS resulting from VUMPS.

[leburgel]

I have this lying around somewhere, but it might take a bit of work to get it in here in a clean way. I'll try to put some work into this soon.

[Yue-Zhengyuan]

Are you somehow able to extend this beyond operators that only acts on sites in the same row / same column? In my past experience, measuring on, e.g. next-nearest neighbors, with a 2-row left/right fixed point costs much more memory than CTMRG.

[leburgel]

The one I have is an exact mirror of the CTMRG expectation value routine, performing an exact contraction of the finite patch using an environment of MPS and environment tensors. So it gets a bit expensive for larger patches, but it doesn't need the full two-row fixed points. At convergence, the two-row fixed point should be given by a product of two (potentially different) single-row fixed point tensors.