SpaceMismatch for the naive gradient evaluation

[Confusio]

I define the following function to evaluate the energy and the gradient by naively using the 10 ctmrg steps to avoid the divergent gradient in the fixed-point method. I don't think I need fix the truncation space and then implement truncdim(χenv) for trscheme.

boundary_alg=SimultaneousCTMRG(;projector_alg=FullInfiniteProjector,trscheme=truncdim(χenv))
function engrad(peps, env, operator,boundary_alg)    
    E, gs = withgradient(peps) do ψ
        for _ in 1:10
            env, _ = ctmrg_iteration(InfiniteSquareNetwork(ψ), env, boundary_alg)
        end
        return cost_function(ψ, env, operator)
    end
    return E, only(gs)
end

However, I got the error

ERROR: LoadError: SpaceMismatch("Vect[(FermionParity ⊠ Irrep[U₁])]((0, 0)=>43, (1, 1/2)=>34, (0, 1)=>15, (1, -1/2)=>34, (0, -1)=>15, (1, 3/2)=>2, (1, -3/2)=>2) ← Vect[(FermionParity ⊠ Irrep[U₁])]((0, 0)=>42, (1, 1/2)=>34, (0, 1)=>15, (1, -1/2)=>34, (0, -1)=>15, (1, 3/2)=>2, (1, -3/2)=>2) ≠ Vect[(FermionParity ⊠ Irrep[U₁])]((0, 0)=>43, (1, 1/2)=>35, (0, 1)=>14, (1, -1/2)=>35, (0, -1)=>14, (1, 3/2)=>2, (1, -3/2)=>2) ← Vect[(FermionParity ⊠ Irrep[U₁])]((0, 0)=>42, (1, 1/2)=>35, (0, 1)=>14, (1, -1/2)=>35, (0, -1)=>14, (1, 3/2)=>2, (1, -3/2)=>2)")
Stacktrace:
  [1] add(ty::TensorMap{ComplexF64, GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep}}, Int64}}, 1, 1, Vector{ComplexF64}}, tx::TensorMap{ComplexF64, GradedSpace{ProductSector{Tuple{FermionParity, U1Irrep}}, TensorKit.SortedVectorDict{ProductSector{Tuple{FermionParity, U1Irrep}}, Int64}}, 1, 1, Vector{ComplexF64}}, α::VectorInterface.One, β::VectorInterface.One)

due to the call of the function

# Functions used for FP differentiation and by KrylovKit.linsolve
function Base.:+(e₁::CTMRGEnv, e₂::CTMRGEnv)
    return CTMRGEnv(e₁.corners + e₂.corners, e₁.edges + e₂.edges)
end

I want to know where the add function for the environment tensors is called in my defined function. I even don't think it is a well defined operation for adding two environment tensors.

[lkdvos]

This is a Zygote thing: we are representing the cotangents of the CTMRGEnv as CTMRGEnv objects (similar to how the cotangent of a Vector is again a Vector).
In other words, Zygote is trying to "retract" the environment here.