SketchedExpand doesn't work on FiniteMPS with a composite physical space (multiple site indices)

[VinceNeede]

Hi all, thanks for all the great work on this package!

I'm building an LPTN library on top of MPSKit, and while testing time evolution with SketchedExpand I ran into an error. Here's a minimal example:

using MPSKit, TensorKit
include("test/setup/testsetup.jl")
using .TestSetup

L = 10
P = ℂ^2
Dummy = ℂ^2
Dstart = 2
Dcap = 16
dt = 0.05

H = heisenberg_XXX(ComplexF64, Trivial; spin = 1 // 2, L)

# site tensors are `GenericMPSTensor{ComplexSpace,3}`: (Vl, P, Dummy) <- Vr
ψ₀ = FiniteMPS(rand, ComplexF64, L, P ⊗ Dummy, ℂ^Dstart)
alg = TDVP(;
    alg_expand = SketchedExpand(; trunc = truncrank(Dstart), oversampling = 4),
    trunc = truncrank(Dcap)
)
for _ in 1:6
    timestep!(ψ₀, H, 0.0, dt, alg)
end

Error message:

ERROR: SpaceMismatch: Direct sum of a vector space and its dual does not exist
Stacktrace:
 [1] ⊕
   @ ~/.julia/packages/TensorKit/zSHBV/src/spaces/complexspace.jl:57 [inlined]
 [2] changebond!(site::Int64, ::Val{…}, ψ::FiniteMPS{…}, H::FiniteMPOHamiltonian{…}, alg::SketchedExpand{…}, envs::MPSKit.FiniteEnvironments{…}; normalize::Bool)
   @ MPSKit ~/MPSKit.jl/src/algorithms/changebonds/sketchedexpand.jl:123
 [3] changebond!
   @ ~/MPSKit.jl/src/algorithms/changebonds/sketchedexpand.jl:92 [inlined]
 [4] timestep!(ψ::FiniteMPS{…}, H::FiniteMPOHamiltonian{…}, t::Float64, dt::Float64, alg::TDVP{…}, envs::MPSKit.FiniteEnvironments{…}; imaginary_evolution::Bool)
   @ MPSKit ~/MPSKit.jl/src/algorithms/timestep/tdvp.jl:156
 [5] timestep!
   @ ~/MPSKit.jl/src/algorithms/timestep/tdvp.jl:120 [inlined]
 [6] timestep!(ψ::FiniteMPS{…}, H::FiniteMPOHamiltonian{…}, t::Float64, dt::Float64, alg::TDVP{…})
   @ MPSKit ~/MPSKit.jl/src/algorithms/timestep/tdvp.jl:120
 [7] top-level scope
   @ ~/MPSKit.jl/trial.jl:22
Some type information was truncated. Use `show(err)` to see complete types.

I think the issue is here:

MPSKit.jl/src/algorithms/changebonds/sketchedexpand.jl

Line 123 in 0ff11c3

nc_space = (codomain(right_tail)[1] ⊕ space(Q, 3)') ← domain(right_tail)

space(Q, 3)' looks like it assumes Q has exactly one physical-like leg, so the flat index 3 happens to land on its new-bond-direction space only when there's a single physical leg. For a state whose site tensors carry more than one physical-like leg (as in my case, GenericMPSTensor{S,3}), index 3 lands somewhere else instead. Since Q always has exactly one domain leg regardless of how many codomain legs it has, I believe domain(Q)[1] is the leg-count-agnostic fix.

I tried this change locally and it resolves the error for me. Happy to open a PR with it if that would help!

[lkdvos]

Ah you are right! I think we also might have a utility _lastspace somewhere, or just right_virtualspace might work. It would be great if you could open a PR and add some tests for this case, but otherwise I'll try and make some time next week