variance() throws SpaceMismatch for real-scalartype long-range InfiniteMPOHamiltonian #524

Summary

variance(::InfiniteMPS, ::InfiniteMPOHamiltonian) throws a SpaceMismatch when the Hamiltonian is real-scalartype and has a long-range (non-nearest-neighbour) term, while the state is complex-scalartype.

Reproduction

using MPSKit, TensorKit
using TensorKit: ℙ

g, D, L = 4.0, 6, 3
H = force_planar(long_range_ising_infinite(Float64; g, L))  # or any real, long-range InfiniteMPOHamiltonian
ψ₀ = InfiniteMPS(fill(ℙ^2, L), fill(ℙ^D, L))
variance(ψ₀, H)  # throws

(long_range_ising_infinite/force_planar are test helpers from test/setup/testsetup.jl; any real, long-range InfiniteMPOHamiltonian combined with a complex state should reproduce this.)

Error

SpaceMismatch: ((ℙ^1 ⊞ ℙ^1 ⊞ ℙ^1) ⊗ ⊞(ℙ^2)) ← (⊞(ℙ^2) ⊗ (ℙ^1 ⊞ ℙ^1 ⊞ ℙ^1)) ≠ ((ℙ^1 ⊞ ℙ^1) ⊗ ⊞(ℙ^2)) ← (⊞(ℙ^2) ⊗ (ℙ^1 ⊞ ℙ^1))
Stacktrace:
  [1] add(ty::BlockTensorKit.SparseBlockTensorMap{TensorMap{Float64, ...}}, tx::BlockTensorKit.SparseBlockTensorMap{TensorMap{ComplexF64, ...}}, ...)
    @ BlockTensorKit ~/.julia/packages/BlockTensorKit/DSAP5/src/tensors/vectorinterface.jl:27
  ...
  [16] +(A::InfiniteMPOHamiltonian{JordanMPOTensor{Float64,...}}, B::InfiniteMPOHamiltonian{JordanMPOTensor{ComplexF64,...}})
    @ Base ./arraymath.jl:8
  [17] -(H1::InfiniteMPOHamiltonian{JordanMPOTensor{Float64,...}}, H2::InfiniteMPOHamiltonian{JordanMPOTensor{ComplexF64,...}})
    @ MPSKit ~/src/operators/mpohamiltonian.jl:1005
  [18] variance(state::InfiniteMPS{...ComplexF64...}, H::InfiniteMPOHamiltonian{JordanMPOTensor{Float64,...}}, envs::...)
    @ MPSKit ~/src/algorithms/toolbox.jl:122

Diagnosis

variance computes something like ⟨H²⟩ - ⟨H⟩² and ends up subtracting two InfiniteMPOHamiltonians: one built by squaring H (which ends up complex, presumably promoted through contraction with the complex environments/state) and one derived from H itself (real). The two InfiniteMPOHamiltonians' shared virtual leg (a SumSpace) end up with a different number of blocks (3 vs 2) once the long-range (1, L) coupling is included, so the elementwise +/- on their JordanMPOTensors hits a genuine structural SpaceMismatch, not just a scalartype-promotion issue.

This reproduces independent of find_groundstate/any optimization algorithm — it's purely in variance's own Hamiltonian arithmetic for long-range + real/complex-mismatched combinations.

Context

Found while adding long-range Hamiltonian coverage to test/groundstate/groundstate.jl in #493. The affected checks there are marked @test_broken referencing this issue.