The normal t-J model restricts occupation to one fermion per site, and hence the charge would be frozen. Your model seems to be a different one?

If the atoms are mobile then the simplest way to enforce the constraint is by a penalty term that penalizes configurations that do not satisfy your constraint. if we call the two densities inside a unit cell n1 and n2, the you want to add a term like U*(n1+n2-2)^2. If you multiply this out then you get, dropping constants:

4*U*(n1+n2) + U*n1^2 + U*n2^2 + 2 U*n1*n2

These terms are just - a chemical potential mu=-4U on each site - a Hubbard repulsion U on each site - an intra-cell repulsion term of strength 2U

By adding these terms to your model and making U large enough (but not too large or accuracy will suffer) you wll restrict yourself to just the sector you desire.

The alternative is to merge the two sites into a single one, with a larger site basis, and then choose the basis to enforce the constraint exactly.

Matthias

On 02 Jan 2014, at 13:42, Elton Nascimento emn@fis.ufal.br wrote:

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.

Elton M. Nascimento