Calculatation code for Von Neumann entropy

DMRG and Numerical Methods
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1

Hi all,

I want to calculate the entanglement entropy of a fermion chain, and I find the following code.
(Entanglement entropy (Julia) - ITensor Support Q&A).
The code is

function entropy_von_neumann(psi::MPS, b::Int)
  s = siteinds(psi)  
  orthogonalize!(psi, b)
  _,S = svd(psi[b], (linkind(psi, b-1), s[b]))
  SvN = 0.0
  for n in 1:dim(S, 1)
    p = S[n,n]^2
    SvN -= p * log(p)
  end
  return SvN
end

I would like to ask if the b mentioned in this program refers to the entanglement entropy of the two subsystems before and after the truncation at b position

But then I see a code that adds a “for loop”. So what does b for i in 2:N-1 mean in this code?

function entropyvonneumann(psi::MPS, N::Int)
    SvN = fill(0.0, N)
    for b in 2:N-1
    orthogonalize!(psi, b)
    _,S = svd(psi[b], (linkind(psi, b-1), s[b]))
    for n in dim(S, 1)
    p = S[n,n]^2
    SvN[b] -= p * log(p)
    end
    println("$(SvN[b])")
    end
    return SvN
end

Please tell me if I need to add a “for loop” if I want to calculate the entanglement entropy of a subsystem that cuts off the first part and the second part at parameter b.

2

I’m not sure what that for loop is doing either, and I did not see any such for loop at the link you provided.

I would recommend you use the code example from our most current documentation here:
<MPS and MPO Examples · ITensors.jl >
In that code, “b” refers to a bond number. So like bond number 1,2,3, … of the MPS. The entanglement computed is between sites 1,2,…b and sites b+1,b+2,…,N. It is the “bipartite von Neumann” entanglement entropy between those two groups of sites.

3

Thank you very much for your answer. I think I understand.