How to calculate von Neumann entropy from MPS

ITensor Julia Questions
1

Hi all. So I am trying to calculate von Neumann entropy (not entanglement entropy, namely I am not trying to bipartite the system) by using the ground state psi after DMRG. The ground state energy matches well with exact diagonalization (ED), so I am trying to find out whether the von Neumann entropy of the density matrix constructed from psi matches that from ED.

I fully realize that there is an official way of computing entanglement entropy from psi provided by itensors team. The code is as following:

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

However, this is not what I want. I am asking how to modify this block of code to calculate just von Neumann entropy. Thanks!

2

Hi, so the code should compute the von Neumann entropy, as defined here:
https://en.wikipedia.org/wiki/Von_Neumann_entropy
If you believe it isn’t, please let us know why not but I think it is.

3

Hi Miles. Thank you! It seems like I have some misunderstanding of the code I posted.

1 Like
4

Can we apply the method for the matrix product density operator (MPDO).

5

If the definition of entropy you are wanting to compute would be the same as if you treated an MPDO as an MPS i.e. a “purification” of the density matrix then yes. However, if you are asking if you can compute the thermodynamic entropy (i.e. the entropy in the formula F = E-TS) this way then no, because that entropy is defined differently.