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
The analytical expression of the correlation function for a free particle is given by
Now if we scale (by a factor say h) such that
i -> hi
j -> hj
kF -> kF/h
G(hi,hj)=sin(kF(i-j))/(pih(i-j)) = G(i,j) / h
Log[G(hi,hj)/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(hi,hj)/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.