Dear Matthias Troyer
You are right, but the lattice we are using shows hop energy between the two sites of the unit cell (edge type = 0) and an exchange energy between sites in adjacent cells (edge type = 1), as bellow
<UNITCELL name="Nascimento" dimension="1">
<VERTEX type="0"/>
<VERTEX type="0"/>
<EDGE type="1"><SOURCE vertex="1"/><TARGET vertex="1" offset="1"/></EDGE>
<EDGE type="1"><SOURCE vertex="2"/><TARGET vertex="2" offset="1"/></EDGE>
<EDGE type="0"><SOURCE vertex="1"/><TARGET vertex="2"/></EDGE>
</UNITCELL>
Because of the hop energy, the particles have transition probability between the sites of the unit cell, but not between adjacent cells. This is why we need ensure the total particles of the unit cell be constant.