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