The first two eigenvalues of the transfer matrix of MPS

[JerryChen97]

As Yin-Chen mentioned before, we can use the second eigenvalue of an MPS' transfer matrix to see if this wavefunction is in a cat state.
So I did this for my current wavefunction data set.

[JerryChen97]

The first fig shows the normalization of the wave functions, which is simply perfectly all one.
In the second figure, the values never reach one except for the gapless points, which is also what we expected: the gapless points have infinite correlation so the second eigenvalue of the transfer matrix will be one.