Add normalize!(::MPS/MPO)

[mtfishman]

Add normalize!(::MPS/MPO). It should normalize just the center sites. Also, it should carefully handle the normalization if the total norm of the MPS/MPO diverges (i.e. for an ungauged MPS/MPO with many sites). It can also return the norm per site.

Perhaps the API could be:

sitenorms = []
normalize!(psi; sitenorms! = sitenorms)

where the norm per site gets appended to the vector sitenorms (to keep the convention that in-place functions return the object being modified).

[mtfishman]

Also to add on: I kind of like the idea of passing outputs that get overwritten as keyword arguments, since it gives more flexibility to the API, like if you want to add more things to get output. In a function like normalize!, you could imagine also returning the log of the total normalization, for example, as a keyword argument lognorm! = lognorm. This function may not be the best example, but other functions like svd or MPS/MPO functions that truncate may have all sorts of different outputs a user might want. Returning them as a tuple kind of locks-in the API, since once you choose the outputs then it is hard to change it without breaking code. Keyword arguments are more flexible.

[mtfishman]

This would be useful in a function like MPS(::ITensor, sites), where you expect it to output the MPS, but then you might also want the Spectrum object for each bond, if truncation is performed, so it would be something like:

s = siteinds("S=1/2", 3)
A = randomITensor(s...)
spectra = []
ψ = MPS(A, s; spectra! = spectra)

so that spectra would store the Spectrum objects for each bond of the MPS.