Fix Multiline (MultilineMPS/MultilineMPO) correctness and API inconsistencies

[borisdevos]

I found a cluster of bugs that all traced back to the same root cause, namely Multiline{T} was inconsistent about what it is. Sometimes it was treated as a 2D array indexed by (row, col), and sometimes as a 1D sequence of T-typed lines, this while different parts of the code picked different conventions without checking consistency. The real bugs were:

• MultilineMPO * MultilineMPS had never worked (straight up method error), and fixing that trivially still left both a shape bug (length counting rows*cols while map/collect only ever produced rows elements) and a silently wrong row-shift bug (fidelity 0 where it should be 1).
• expectation_value(::MultilineMPS, ::MultilineMPO, ...) had a fallback method that silently returned something meaningless (prod instead of sum, no row shift, discarded envs which was noted through a todo) for any MultilineMPO line type it wasn't explicitly guarded against. Related to this, there was half-support for Hamiltonian or finite MPO multilines even though they're meaningless. Also the environments weren't being correctly converted, so they were being recalculated every row.
• isfinite, changebonds(::MultilineMPO, ::SvdCut), and axes(m, 2) all threw outright.

A summary of the changes I made:

"Semantics":

• Multiline{T} now consistently treats length/eltype/iterate/m[i] as referring to the lines (matching the periodic rows), while size/axes/eachindex refer to the (nrows, ncols) lattice shape. These two views are intentionally different (length(m) != prod(size(m))). I also documented this in docstrings.
• Fixed multiplication: both were broken. The row-shifting is implemented and documented.
• Deleted the expectation_value fallback. Changed the infinite MPS-MPO expectation value to correctly account for environments.
• Fixed isfinite, changebonds(::MultilineMPO/::MultilineMPS, ::SvdCut), and axes(m, i).
• Some grassmann code needed a change related to the 1d vs 2d view thing above.
• Added the missing instance-level spacetype/sectortype/storagetype for multiline. I needed this for the custom show (see below).

Construction restrictions:

• MultilineMPO only accepts InfiniteMPO lines now, enforced at constructor level. This is deliberate, since Multiline is also used via converts in environments, quasiparticles etc.
• Removed the AbstractMatrix constructor that silently built finite-line MultilineMPOs, and the dead code in orthoview.jl that existed only to support finite MPS multilines.

Display:

• MultilineMPS/MultilineMPO custom show: added a summary which looks at the 2d shape, and a show that renders each row using that row's own existing show method. Here below an example of how it looks now:

Here the multiline MPS:

Details

2×2 MultilineMPS(ComplexF64, Vect[IsingAnyon]) with maximal dimension 10.0:
row 1:
2-site InfiniteMPS(ComplexF64, Vect[IsingAnyon]) with maximal dimension 10.0:
| ⋮
| (:σ => 7)
├─[2]─ (:σ => 1)
│ (:I => 5, :ψ => 5)
├─[1]─ (:σ => 1)
│ (:σ => 7)
| ⋮

  ⋮
row 2:
2-site InfiniteMPS(ComplexF64, Vect[IsingAnyon]) with maximal dimension 10.0:
| ⋮
| (:I => 5, :ψ => 5)
├─[2]─ (:σ => 1)
│ (:σ => 7)
├─[1]─ (:σ => 1)
│ (:I => 5, :ψ => 5)
| ⋮

And here a multiline MPO:

Details

2×2 MultilineMPO(ComplexF64, Vect[IsingAnyon]) with maximal dimension 1.4142135623730951:
row 1:
2-site InfiniteMPO(ComplexF64, Vect[IsingAnyon]) with maximal dimension 1.4142135623730951:
| ⋮
| (:σ => 1)
┼─[2]─ (:σ => 1)
│ (:σ => 1)
┼─[1]─ (:σ => 1)
│ (:σ => 1)
| ⋮

  ↓  (row 1 maps onto row 2)
row 2:
2-site InfiniteMPO(ComplexF64, Vect[IsingAnyon]) with maximal dimension 1.4142135623730951:
| ⋮
| (:σ => 1)
┼─[2]─ (:σ => 1)
│ (:σ => 1)
┼─[1]─ (:σ => 1)
│ (:σ => 1)
| ⋮

  ↓  (row 2 maps onto row 1)

Tests:

• New test/operators/multilinempo.jl: exact-fidelity tests for the row-shift convention in both MultilineMPO * MultilineMPS and MultilineMPO * MultilineMPO, using a permutation MPO whose fixed point is known exactly.
• test/algorithms/statmech.jl: multi-row expectation_value regression test. Also a test that the Hamiltonian loophole above still correctly throws.
• test/states/multilinemps.jl: added instance-level isfinite(ψ) (only the type-level form was covered before).

Documentation:

• docs/src/man/states.md: added the row-shift convention, what's currently supported (infinite lines only), and subtleties.
• docs/src/man/operators.md: new MultilineMPO section covering the same convention, and emphasising the MPO*MPO non-composability caveat.
• Updated docstrings on Multiline, MultilineMPO, MultilineMPS, and expectation_value.
• Added to the changelog, as the PR template wished of me 😄 .

Some things I didn't address because I'm not sure what to do with them:

• VectorInterface stuff is still broken for MultilineMPS, simply because InfiniteMPS itself doesn't implement zerovector/scale.
• norm(ψ) == sqrt(nrows) for a MultilineMPS of individually-normalized rows is unchanged. This goes through dot/inner sum over rows. I don't know if this is what you want.

Checklist

• Tests pass locally (julia --project=test test/runtests.jl, or the relevant subset)
• Documentation updated, if this PR changes public API (docstrings, docs/src/)
• Runic formatter is run
• Changelog entry added under [Unreleased] in docs/src/changelog.md, if this PR is user-facing (new feature, behavior change, bug fix, deprecation, or removal)

[codecov]

Codecov Report

❌ Patch coverage is 28.35821% with 48 lines in your changes missing coverage. Please review.

Files with missing lines	Patch %	Lines
src/utility/show.jl	0.00%	36 Missing ⚠️
src/utility/multiline.jl	50.00%	5 Missing ⚠️
src/algorithms/changebonds/svdcut.jl	60.00%	2 Missing ⚠️
src/algorithms/expval.jl	50.00%	2 Missing ⚠️
src/environments/multiline_envs.jl	50.00%	1 Missing ⚠️
src/operators/multilinempo.jl	80.00%	1 Missing ⚠️
src/states/orthoview.jl	50.00%	1 Missing ⚠️

Files with missing lines	Coverage Δ
src/algorithms/changebonds/randexpand.jl	63.63% <100.00%> (+35.06%)	⬆️
src/algorithms/grassmann.jl	79.03% <100.00%> (+79.03%)	⬆️
src/states/multilinemps.jl	81.39% <ø> (+34.72%)	⬆️
src/environments/multiline_envs.jl	80.35% <50.00%> (+80.35%)	⬆️
src/operators/multilinempo.jl	72.72% <80.00%> (+52.72%)	⬆️
src/states/orthoview.jl	89.17% <50.00%> (+25.53%)	⬆️
src/algorithms/changebonds/svdcut.jl	89.18% <60.00%> (+13.51%)	⬆️
src/algorithms/expval.jl	87.35% <50.00%> (+39.12%)	⬆️
src/utility/multiline.jl	63.49% <50.00%> (+42.18%)	⬆️
src/utility/show.jl	12.30% <0.00%> (-2.79%)	⬇️

... and 59 files with indirect coverage changes

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