How to perform a kronecker product of two MPSs

[hainingpan]

How can I create a new MPS which is the “concantenation” (kronecker product) of two MPSs?
Namely, say MPS1 is a random MPS, and MPS2 is simply |0>. Then I want to create a new MPS being |0>|MPS1>.

The minimal example is:

s1=siteinds("Qubit", 4)
mps1= randomMPS(s;linkdims=3)

s2=siteinds("Qubit", 1)
mps2 = MPS(s2, ["0"])   

# mps = kron(mps2, mps1) ?

I understand that, mathematically, it is just that I need to create a singleton axis for the mps2 on the right and for mps1 on the left. But how do I achieve that in ITensors?

I notice a similar question is mentioned in

Tensor product together MPS

A good way to do this in ITensor would be to make a new MPS with n qubits and then assign the MPS tensors of \ket{r} to the sites j=2,3,4,...,n of this MPS and then set the first MPS tensor to the \ket{0} state. I’d do it in the following way: make the set of qubit indices s = siteinds("Qubit",n) make \ket{r} by calling r = randomMPS(s[2:n]; linkdims=chi) make an MPS psi = MPS(s,"0") of qubits all in the \ket{0} state finally, write a for loop that just assigns the tensors of the MPS \ket{r} …

However, what I cannot figure out is to make the “index” match. I guess that has to be done in Step 4

4. finally, write a for loop that just assigns the tensors of the MPS ∣r⟩\ket{r}∣r⟩ to the appropriate tensors of psi

But the naive method doesn’t work

for i in 2:N
    mps[i] = mps1[i-1]
end

because it will miss the link between mps[1] and mps[2].

And I also try to “manually” copy only the data of tensor but not the index through

mps=MPS(vcat(s1,s2),"0")

for idx in 2:n
    if idx == 2
        arr=array(mps1[idx-1])

        mps[idx] = ITensor(reshape(arr,(1,size(arr)...)),inds(mps[idx]))
    else
        mps[idx]=ITensor( array(psi1[idx-1]) , inds(mps[idx]))
    end
end

which also fails:

DimensionMismatch: In ITensor(::AbstractArray, inds), length of AbstractArray (6) must match total dimension of IndexSet (2)

Stacktrace:
 [1] ITensor(as::NDTensors.NeverAlias, eltype::Type{Float64}, A::Array{Float64, 3}, inds::Tuple{Index{Int64}, Index{Int64}, Index{Int64}}; kwargs::@Kwargs{})
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:352
 [2] ITensor
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:345 [inlined]
 [3] #ITensor#136
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:411 [inlined]
 [4] ITensor
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:408 [inlined]
 [5] #ITensor#138
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:421 [inlined]
 [6] ITensor(A::Array{Float64, 3}, is::Tuple{Index{Int64}, Index{Int64}, Index{Int64}})
   @ ITensors ~/.julia/packages/ITensors/UHeB1/src/itensor.jl:420
 [7] top-level scope
   @ ./In[163]:8