Implementation of Dice lattice in GFTool

[andrewkhardy]

thanks for making this package as I've found the eliptic integrals for DOS very convenient. I'm wondering if you could add the "dice" lattice, dual to the Kagome to your long list of lattices?

The Hamiltonian in k-space and the resulting dispersion is given in Eq. 2 and the text beneath it of this paper. Thanks in advance!

[DerWeh]

Sorry for the slow response @andrewkhardy, I was gone for quite a while and the notification is buried in unread mails...

Of course, we can add the dice lattice. If you like, you can of course write a pull request yourself.
Else, I hope to find some time this weekend.

I have to check your reference. For the DOS we can probably readily use eq. (13) of Varma and Monien (2013), as it's expressed in terms of the triangular lattice which is already implemented.
Is the special case \gamma=1 (all hoppings equal) enough, or are you interested in the more general case?

[DerWeh]

I worked through the equations, and to me, it seems that the diced lattice Green's function is nothing but (2/3) the honeycomb lattice Green's function plus the dispersionless contribution 1/3z (corresponding to the delta peak of magnitude 1/3 in the DOS at 0).

In this case, the implementation would be rather trivial:

def gf_z(z, half_bandwidth):
    return 1/3*z + 2/3*gt.lattice.honeycomb.gf_z(z, half_bandwidth)


def dos(eps, half_bandwidth):
    """As usual, we exclude the delta peak."""
    return 2/3*gt.lattice.honeycomb.dos(z, half_bandwidth)

Can you please confirm @andrewkhardy? I simply compared the equations in Varma and Monien (2013) with the equations in Tsuyoshi Horiguchi (1972). I never studied the diced lattice, so please confirm, then I will implement it.