Hi,

I am trying to understand how lattices are defined in ALPS and am having some difficulties. For example the hexagonal lattice from the lattices.xml that comes with ALPS (1.3b6) has dimension 2 but then the basis vectors and reciprocal basis vectors are 3 dimensional.

<LATTICE name="hexagonal lattice" dimension="2"> <PARAMETER name="a" default="1"/> <PARAMETER name="c" default="1"/> <BASIS> <VECTOR>a 0 0</VECTOR> <VECTOR>a/2 a*sqrt(3)/2 0</VECTOR> <VECTOR>0 0 c</VECTOR> </BASIS> <RECIPROCALBASIS> <VECTOR>2*pi/a -2*pi/a/sqrt(3) 0 </VECTOR> <VECTOR>0 4*pi/a/sqrt(3) 0 </VECTOR> <VECTOR>0 0 2*pi/c</VECTOR> </RECIPROCALBASIS> </LATTICE>

Maybe I'm not getting how a lattice can be defined by basis vectors. Are there any good resources online about this? I have looked at the ALPS wiki but the images are missing from the pages about lattice definitions.

Also how can one specify the extent in each direction and the boundary conditions for the above lattice? Also how will the vertices be numbered?

Any help is much appreciated.

Kind Regards,

Niall.