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