Hi,

I don’t know which problems you get and what you mean by "I still can't follow Fig4(b)”, but a quick look at the model below shows that yu implemented it differently than we implemented the bosonic Hubbard model in he default models.xml file. Is there a reason for that? And what code are you using?

If you want to test your model implementation and lattice then I would suggest that you first do a tiny lattice that you ca solve exactly and test the individual terms separately

Matthias Troyer

On Jan 27, 2016, at 1:38 AM, 北尘心 740572900@qq.com wrote:

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 !

---

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;}

---

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> ------------------------------------------------------------------------------------------------------------- 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> -------------------------------------------------------------------------------------------------------------

Best regards,

Xiaofan Zhou