Dear all, I want to use 2 band chain lattice (there are three edge types in unitcell) in my hubbard model which is in lattices.xml file. I build the lattice according to guidance in the website:
<LATTICES> <LATTICE name="chain lattice" dimension="1"> <PARAMETER name="a" default="1"/> <BASIS><VECTOR>a</VECTOR></BASIS> <RECIPROCALBASIS><VECTOR>2*pi/a</VECTOR></RECIPROCALBASIS> </LATTICE>
<UNITCELL name="2band1d" dimension="1"> <VERTEX type="0"/> <VERTEX type="1"/> <EDGE type="0"><SOURCE vertex="1" offset="0"/><TARGET vertex="2" offset="0"/></EDGE> <EDGE type="1"><SOURCE vertex="1" offset="0"/><TARGET vertex="1" offset="1"/></EDGE> <EDGE type="2"><SOURCE vertex="2" offset="0"/><TARGET vertex="2" offset="1"/></EDGE> </UNITCELL>
<LATTICEGRAPH name = "2 band chain lattice"> <FINITELATTICE> <LATTICE ref="chain lattice"/> <EXTENT dimension="1" size ="L"/> <BOUNDARY type="periodic"/> </FINITELATTICE> <UNITCELL ref="2band1d"/> </LATTICEGRAPH>
</LATTICES>
Because there are three edge types in unitcell , i wonder what I should do to design hopping in my model. I design two solutions ,like : <HAMILTONIAN name="boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t0" default="1"/> <PARAMETER name="t1" default="2"/> <PARAMETER name="t2" default="3"/> <PARAMETER name="U" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> -mu*n(i)+U*bdag(i)*bdag(i)*b(i)*b(i)/2 </SITETERM> <BONDTERM type="0" source="i" target="j"> -t0*(bdag(i)*b(j)+bdag(j)*b(i)) </BONDTERM> <BONDTERM type="1" source="i" target="j"> -t1*(bdag(i)*b(j)+bdag(j)*b(i)) </BONDTERM> <BONDTERM type="2" source="i" target="j"> -t2*(bdag(i)*b(j)+bdag(j)*b(i)) </BONDTERM> </HAMILTONIAN>
and
<HAMILTONIAN name="boson Hubbard"> <PARAMETER name="mu" default="0"/> <PARAMETER name="t0" default="1"/> <PARAMETER name="t1" default="2"/> <PARAMETER name="t2" default="3"/> <PARAMETER name="U" default="0"/> <BASIS ref="boson"/> <SITETERM site="i"> -mu*n(i)+U*bdag(i)*bdag(i)*b(i)*b(i)/2 </SITETERM> <BONDTERM source="i" target="j"> -t0*(bdag(i)*b(j)+bdag(j)*b(i))-t1*(bdag(i)*b(j)+bdag(j)*b(i))-t2*(bdag(i)*b(j)+bdag(j)*b(i)) </BONDTERM> </HAMILTONIAN>
I want to know my two design which one is correct?
Yours sincerely,
Xingbo Wei Zhejiang Normal Universtiy, Jinhua, 230014, China