Failure in addition of InifiniteMPOHamiltonian

[Gertian]

Hi,

I'm playing around with the newest update of MPSKit and it seems that I've been able to make an InfiniteMPOHamiltonian for which the addition fails.
(MPSKit, TensorKit and BlockTensorKit are all on the latest master)

A MWE is :

using TensorKit, MPSKit
#the symmetry group
sym = (U1Irrep ⊠ U1Irrep ⊠ FermionParity)
#some relevant irreps
∅ = sym.(0, 0, 0)
ψ1 = sym.(3, 0, 1)  
ψ2 = sym.(4, 5, 1)  
ψ3 = sym.(5, 4, 1)  
ψ4 = sym.(0, 3, 1)  
ψ = [ψ1, ψ2, ψ3, ψ4]
#physical Hilbert spaces
P1 = Vect[sym](∅ => 1, ψ1 => 1) #the physical space is build from the space spanned by the empty and full site.
P2 = Vect[sym](∅ => 1, ψ2 => 1) #the physical space is build from the space spanned by the empty and full site.
P3 = Vect[sym](∅ => 1, ψ3 => 1) #the physical space is build from the space spanned by the empty and full site.
P4 = Vect[sym](∅ => 1, ψ4 => 1) #the physical space is build from the space spanned by the empty and full site.
P = [P1, P2, P3, P4]

#some more relevant irreps
ψ1hop = sym.(3, 0, 1)
ψ2hop = sym.(4, 5, 1)
ψ3hop = sym.(5, 4, 1)
ψ4hop = sym.(0, 3, 1)
ψhop = [ψ1hop, ψ2hop, ψ3hop, ψ4hop]
#and vector spaces
V1 = Vect[sym](ψ1hop => 1, dual(ψ1hop) => 1) 
V2 = Vect[sym](ψ2hop => 1, dual(ψ2hop) => 1) 
V3 = Vect[sym](ψ3hop => 1, dual(ψ3hop) => 1) 
V4 = Vect[sym](ψ4hop => 1, dual(ψ4hop) => 1)
V = [V1, V2, V3, V4]

#Some operators
function K(ϕ, flavour)
    KL = TensorMap(zeros, ComplexF64, P[flavour] ← P[flavour] ⊗ V[flavour])
    block(KL, ψ[flavour]) .= exp(-im * ϕ)           
    block(KL, ∅        ) .= exp(+im * ϕ)           

    KR = TensorMap(zeros, ComplexF64, V[flavour] ⊗ P[flavour] ← P[flavour])
    block(KR, ψ[flavour]) .= 1                            
    block(KR,∅         )  .= 1

    @planar Kres[-1 -2; -3 -4] := KL[-1; -3 3] * KR[3 -2; -4]
    return Kres
end

#a lattice 
lattice = PeriodicArray(repeat([P1, P2, P3, P4] ,4)) 
# ... -- 5,6,7,8 -- 9,10,11,12  -- 21,22,23,24 -- ...
#        |          |              |
# ... -- 1,2,3,4 -- 13,14,15,16 -- 17,18,19,20 -- ...
NNN_pos_links = [ (1,9) , (5,13) ]

#the thing that is not working : 
H = sum(InfiniteMPOHamiltonian(lattice, (i + (flavour - 1),j + (flavour - 1))=>K(0., flavour) for (i, j) in NNN_pos_links ) for flavour = 1:4)

#a simpler example is : 
flavour = 1
H_mini = InfiniteMPOHamiltonian(lattice, (i + (flavour - 1),j + (flavour - 1))=>K(0., flavour) for (i, j) in NNN_pos_links )
H_mini  + H_mini #does not work

#It seems like the problem comes from : 
H_mini.W #works fine 
H_mini.A #does not work and this is called on the line where the addition fails. I have no clue what this is supposed to do though...

[lkdvos]

Thanks for catching that. Should be addressed in #213.
For the explanation of .A, this, together with .B, .C and .D, are the different blocks in the Jordan MPO:

$$W = \begin{pmatrix} 1 & C & D \\\ 0 & A & B \\\ 0 & 0 & 1 \end{pmatrix}$$

[Gertian]

Thanks for the quick fix and explanation behind the .A .
What happens when the MPOtensor has more then 3by3 blocks though ?

[lkdvos]

then A is a blocktensor itself 😉 .
This is less of a specific tensor, and more of a group of tensors that can be interpreted the same way. All parts of C imply the start of an operator, B is the end, A is the middle, and D is one-site operators

[Gertian]

Ok, very nice :) !