How to calculate the norm per site of an iTPS ?

Hi everyone,

I have a question about the norm of an iTPS. I try to consider a 2D square lattice with size $M\times N$, where the quantum state is described by a infinite-size translation-invariant iTPS $\vert \Psi \rangle$.

To make my question clear, I have found a figure in the "TeNeS-master/docs/sphinx/img" directory and I have attached it as follows.

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It is expected that the norm can be expressed as $$\langle \Psi \vert \Psi \rangle = k^{M\times N},$$ where $k$ is called "the norm per site".

My question is how to figure out this coefficient $k$ ?

In file "01_transverse_field_ising/output/onesite_obs.dat", it reads

The meaning of each column is the following: $1: op_group $2: site_index $3: real $4: imag The names of op_group are the following: 0: Sz
1: Sx
-1: norm 0 0 1.43822572220935002e-01 0.00000000000000000e+00 0 1 1.43822567502205789e-01 0.00000000000000000e+00 0 2 1.43822577490189368e-01 0.00000000000000000e+00 0 3 1.43822572827914413e-01 0.00000000000000000e+00 1 0 4.51957838213799423e-01 0.00000000000000000e+00 1 1 4.51957837144178809e-01 0.00000000000000000e+00 1 2 4.51957758107002339e-01 0.00000000000000000e+00 1 3 4.51957756949986855e-01 0.00000000000000000e+00 -1 0 8.02176941013978739e-01 0.00000000000000000e+00 -1 1 8.02176538960576391e-01 0.00000000000000000e+00 -1 2 8.02178199879971077e-01 0.00000000000000000e+00 -1 3 8.02177795112917202e-01 0.00000000000000000e+00

For the last four lines, the number "8.02e-01" seems to be obtained by simple contracting the corner transfer matrices and the edge tensors in Fig. (c), and its role seems to be the norm of the reduced density matrices for the local $2\times 2$ sub-squares.

Thus, my question is that, is it possible to figure out the coefficient $k$ ? I guess $k$ is still closely related to Fig. (c) in some way, but I am not sure about the details.

Any suggestion or comment would be greatly appreciated.

issp-center-dev / TeNeS

How to calculate the norm per site of an iTPS ? #95