Dear sir,
I am dealing with cubic lattice with first nearest neighbour hopping in all
directions but second nearest neighbour hopping only in z-direction.
Like *c_{j}^{/dagger}
c_{j+2a/hat{z}} /sigma_0 + h.c*. So I get *cos(2k_z)* term in the
Hamiltonian. If I expand this cosine term in polynomial form upto second
order. The discretizer does not give any second neighbour hopping term like
Hoppingkind(0,1, 1). The discretizer mix it with the first nearest
neighbour hopping in z-direction. but If I write the cosine term like
[exp(i2k_z)+exp(-i2k_z)]/2. So I have to assign 0.5 /sigma_0 to the
Hoppingkind(0 1 1) and other similar type of second neighbour hoppings only
in z direction. I am confused that which is the correct way to deal with
this problem. I hope you understand what I mean.
Thank you.
Best Regards
Naveen Yadav
Research Scholar
Department of Physics & Astrophysics
University of Delhi
New Delhi-110007
On Sat, Aug 8, 2020, 18:52 <ousmane...@kaust.edu.sa> wrote:
> Dear Naveen,
> In a square lattice for instance \exp(2 i\pm k.r) would rather correspond
> to a third nearest neighbor.
> This may be the reason of the discrepancy you observe.
>
> Regards,
> Ousmane
>
