Embedding a tensor into a higher order tensor

[leobb]

Hello all! I’m new to ITensor and Tensor Networks so I’d greatly appreciate any help.

My problem is this: I currently have a predefined ITensor, A (2x2x2) which has been extracted from an MPS (psi) at site 3:

A = psi[3]

I would like to embed this tensor into a 4th order (2x2x2x2) zero tensor, T:

i = Index(2, "i")
j = Index(2, "j")
k = Index(2, "k")
l = Index(2, "l")
T = ITensor(i,j,k,l)

Once I embed A into T, the resulting tensor should be a 4th order tensor of dimension (2x2x2x2) (call it G). G should have the structure G[:,:,:,1] = A, and G[:,:,:,2] = a 3rd order (2x2x2) zero tensor. This means that a slice of G contains A, and the other slice contains the 3rd order zero tensor.

I’ve tried:

T[l => 1] = A

where I imagine that A is being embedded in the 1st slice of the last dimension of T (Where A is actually embedded is arbitrary). However, I get the following error:

MethodError: no method matching setindex!(::ITensor, ::ITensor, ::Pair{Index{Int64}, Int64})

My question is: How can I embed a 3rd order tensor A (2x2x2) into a 4th order zero tensor T (2x2x2x2) to achieve an output of a 4th order tensor (2x2x2x2) with the structure specified by G.

I hope this is clearly explained. Please let me know if you require more context (or a better explanation).

Thank you all!

[ryanlevy]

I would suggest instead of slicing, try multiplying by onehot

using ITensors
i, j, k, l = Index.((2, 2, 2, 2))

A = random_itensor(i, j, k)
G = A * onehot(l => 1)

# double check:
Aarray, Garray = array(A, i, j, k), array(G, i, j, k, l)
@show Aarray ≈ Garray[:, :, :, 1]
@show Aarray * 0 ≈ Garray[:, :, :, 2]

output:

Aarray ≈ Garray[:, :, :, 1] = true
Aarray * 0 ≈ Garray[:, :, :, 2] = true

[leobb]

Thanks ryan, this solves my issue

[mtfishman]

An alternative is the ITensors.directsum function.

[leobb]

Thanks Matt, just tried this and works perfectly fine too!