I am using the code for calculating the correlation functions of a free

particle in 1 D using the itensor available codes by only keeping the kinetic energy term without impurity or interactions using the codes

https://github.com/ITensor/ITensor/blob/master/sample/exthubbard.cc http://itensor.org/docs.cgi?page=formulas

The analytical expression of the correlation function for a free particle is given by

G(i,j)=sin(kF(i-j))/(pi(i-j)).

Now if we scale (by a factor say h) such that

i -> h*i
j -> h*j

kF -> kF/h

then

G(h*i,h*j)=sin(kF(i-j))/(pi*h*(i-j)) = G(i,j) / h

OR

Log[G(h*i,h*j)/G(i,j)] = - log[h]

Now I am doing for 100 sites and quarter filling, i.e. No. of particles =

50. When I plot Log[G(h*i,h*j)/G(i,j)] vs log[h], I should get a straight

line with slope -1.

But I am not getting a line quite straight and when I do a least square

fit, I get a slope of -.029 for 10 sweeps and -0.43 for 100 sweeps. Should

I increase the number of sweeps to more and expect it to go to -1,

although this is computationally quite expensive. I just wanted to make sure that I am doing the free particle case correctly so that I can proceed to more complicated things.