I’m new to tensor networks. I understand that for an MPS state in the form of orthogonalization, the bipartite entanglement entropy of a subsystem is center site’s singular spectrum. I’ve found useful code on ITensors.jl 's example:

orthogonalize!(psi, b)
U,S,V = svd(psi[b], (linkind(psi, b-1), siteind(psi,b)))
SvN = 0.0
for n=1:dim(S, 1)
p = S[n,n]^2
SvN -= p * log(p)
end

and have been using them without any issues still I needed to calculate the entropy for an open boundary condition MPS with the first site as the subsystem, there is no longer the ‘b-1’ index. How can I calculate the entropy for this system? Can I directly calculate singular spectrum for ‘psi[1]’? Additionally, is it possible to use the first lattice site as the center for orthogonalization?

That’s the right code to be using. What it will do is compute the entanglement across the b’th bond, so between the sites (1,2,…,b) and (b+1,b+2, …, N).

But I see the issue you mean for the case of b=1, because the function linkind(psi,b-1) will fail in that case. So you will need to fix or generalize that part for that case. A fix could be:

if b==1
U,S,V = svd(psi[b], (siteind(psi,b),))
else
U,S,V = svd(psi[b], (linkind(psi, b-1), siteind(psi,b)))
end

and the rest of the code otherwise. Please give that a try and let us know if it doesn’t work for the b=1 case.

Also there is a more specialized user support & discussion forum about ITensor here if you’d like to ask us questions there: https://itensor.discourse.group