Dear ALPS community,
I have some problems about sawtooth lattice, which is shown in paper 'Bose condensation in flat bands (PhysRevB.82.184502)'. After having canvassed the ALPS tutorial, I construct an one-dimensional lattice with nearest-nearest neighbor hopping and next-nearest neighbor hopping, which is equivalent to the sawtooth lattice. Unfortunately, I still can't follow Fig4(b) of Phys. Rev. B 82, 184502 (2010). The job, lattices.xml and models.xml are shown as follows. I don't know what's wrong with my codes. Could you give me any suggestions ? Thank you very much !
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job:
LATTICE_LIBRARY="lattices.xml"
MODEL_LIBRARY="models.xml"
LATTICE="sawtooth open chain lattice";
MODEL="sawtooth boson Hubbard";
SWEEPS=20;
MAXSTATES=200;
T=0;
t=1.0
t'=sqrt(2)
U=1.0;
MEASURE_LOCAL[n_density]=n
MEASURE_CORRELATIONS[n_correlation]="n:n"
CONSERVED_QUANTUMNUMBERS="N";
{L=40,N_total=20,Nmax=20;}
{L=40,N_total=21,Nmax=21;}
{L=40,N_total=22,Nmax=22;}
{L=40,N_total=23,Nmax=23;}
{L=40,N_total=24,Nmax=24;}
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lattice.xml:
<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="sawtooth" dimension="1">
<VERTEX id="1" type="0"><COORDINATE>0 </COORDINATE></VERTEX>
<VERTEX id="2" type="1"><COORDINATE>0.5 </COORDINATE></VERTEX>
<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="1" offset="1"/></EDGE>
</UNITCELL>
<LATTICEGRAPH name = "sawtooth open chain lattice">
<FINITELATTICE>
<LATTICE ref="chain lattice"/>
<EXTENT dimension="1" size ="L"/>
<BOUNDARY type="open"/>
</FINITELATTICE>
<UNITCELL ref="sawtooth"/>
</LATTICEGRAPH>
</LATTICES>
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model.xml:
<SITEBASIS name="boson">
<PARAMETER name="Nmax" default="infinity"/>
<QUANTUMNUMBER name="N" min="0" max="Nmax"/>
<OPERATOR name="bdag" matrixelement="sqrt(N+1)">
<CHANGE quantumnumber="N" change="1"/>
</OPERATOR>
<OPERATOR name="b" matrixelement="sqrt(N)">
<CHANGE quantumnumber="N" change="-1"/>
</OPERATOR>
<OPERATOR name="n" matrixelement="N"/>
</SITEBASIS>
<HAMILTONIAN name="sawtooth boson Hubbard">
<PARAMETER name="t" default="1"/>
<PARAMETER name="t'" default="0"/>
<PARAMETER name="U" default="0"/>
<BASIS ref="boson"/>
<SITETERM site="i">
U*bdag(i)*bdag(i)*b(i)*b(i)/2
</SITETERM>
<BONDTERM type="0" source="i" target="j">
-t'*(bdag(i)*b(j)+bdag(j)*b(i))
</BONDTERM>
<BONDTERM type="1" source="i" target="j">
-t*(bdag(i)*b(j)+bdag(j)*b(i))
</BONDTERM>
<BONDTERM type="2" source="i" target="j">
-t'*(bdag(i)*b(j)+bdag(j)*b(i))
</BONDTERM>
</HAMILTONIAN>
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Best regards,
Xiaofan Zhou