[discussion] `correlation length` interface

[ogauthe]

This is a follow-up to #199 and #212 .

With #212 , correlation_length(ψ, env; sector=sector) now returns a correct value. By default, sector is the trivial sector.

As discussed, I find it slightly misleading that by default the returned correlation length may not be the largest one (see AKLT test). Especially that it depends on which symmetry is implemented: in the AKLT example, correlation_length(ψ, env) returns 2 different results depending whether ψ makes use of U(1) or SU(2). As a user, I would expect that it returns the largest one by default, then sector is an advanced mode with finer control.

I would expect that if no sector is specifically required, PEPSKit computes eigenvalues in all sectors and returns the larger correlation length.

[lkdvos]

From a practical point of view, I would argue that if we're computing the correlation length in all sectors anyways, we might as well return them, or at least have an interface for that.

On a separate note, I would really like it if correlation_length doesn't actually return the transfer matrix spectra. If one would like the transfer matrix spectrum, the transfer_spectrum function should be used instead.

Finally, I don't think it makes sense to always compute the correlation length both horizontally and vertically. I would suggest to add a (keyword) argument to specify the direction instead, and default to horizontal. I think that as long as we clearly state this, having to explicitly call correlation_length twice in order to obtain both directions is not unreasonable.

Given all of these comments, I would propose something like:

correlation_lengths(psi, [env]; kwargs...) -> SectorDict(sector => xi)
correlation_length(psi, [env]; sector=nothing, kwargs...) -> Float64

where the second one finds the dominant one if sector=nothing, and a specific one if sector=some_sector. The [env] argument is only optional for MPS, and would have to be specified in the peps cases.