Re: [ALPS-users] complex hopping and site dependent parameters
* *>* 1.For a 1D Hubbard model with a complex 't' (hopping) parameter, is *>* it ok to make t complex in the input file?I actually did a run where *>* I used the following input file for the full diagonalization: *>* *>* LATTICE="open chain lattice"; *>* LATTICE_LIBRARY="/home/aakande/alps-applications-1.3.3/tutorial/ *>* lattices.xml" *>* SWEEPS=5 *>* MAXSTATES=30 *>* CONSERVED_QUANTUMNUMBERS="Nup,Ndown" *>* { *>* MODEL="fermion Hubbard"; *>* MODEL_LIBRARY="/home/aakande/alps-applications-1.3.3/tutorial/ *>* models.xml" *>* L=4, Nup_total=1, Ndown_total=1 *>* t=exp(I*5) *>* U=4 *>* NUMBER_EIGENVALUES=1 *>* }
* 2.How does one adjust the input file for a site dependent parameters *>* model?For example, I am interested in a 1D Hubbard model with 10- *>* site chain for which the U term on the first 5 sites are different *>* from the remaining 5 sites (ie 1st 5 sites have U=U1 and the last 5 *>* sites have U=U2) with a different hopping parameter linking the 2 *>* sets of sites.What will change in the input file for such a site *>* dependent model?
Thanks Prof. Mattias, Yes I mean hopping t in one direction and the complex conjugate in the other.It actually worked pretty well for the half filled case (Maybe for the wrong reason or it's just by coincidence) at least with my comparison with BA solutions.Other fillings are screwed up. Thanks once again. Adrian, would u like to comment on DMRG for complex Hamiltonian?Thanks Akin * This will actually not work since if all hoppings are t the model is not Hermitian. Do you mean a model with hopping t in one direction and the complex conjugate in the other? Yes.It actually worked pretty well for a half filled case (Maybe for a wrong reason or it's by coincidence). * You have to build a graph and not a lattice, and give different types to the various sites (vertices) and bonds (edges). You can then specify different t for the bonds and U for the sites. Matthias
You need to go into the models.xml file and look for the hopping term. There you will see that it is the same term in both directions. You should instead define a tl and tr term or similar and set one to I and the other to -I Matthias On Nov 26, 2008, at 3:06 PM, Akinlolu Akande wrote:
Thanks Prof. Mattias,
Yes I mean hopping t in one direction and the complex conjugate in the other.It actually worked pretty well for the half filled case (Maybe for the wrong reason or it's just by coincidence) at least with my comparison with BA solutions.Other fillings are screwed up.
Thanks once again.
Adrian, would u like to comment on DMRG for complex Hamiltonian?Thanks
Akin
1.For a 1D Hubbard model with a complex 't' (hopping) parameter, is it ok to make t complex in the input file?I actually did a run where I used the following input file for the full diagonalization:
LATTICE="open chain lattice"; LATTICE_LIBRARY="/home/aakande/alps-applications-1.3.3/tutorial/ lattices.xml" SWEEPS=5 MAXSTATES=30
CONSERVED_QUANTUMNUMBERS="Nup,Ndown" { MODEL="fermion Hubbard"; MODEL_LIBRARY="/home/aakande/alps-applications-1.3.3/tutorial/ models.xml"
L=4, Nup_total=1, Ndown_total=1 t=exp(I*5) U=4 NUMBER_EIGENVALUES=1 }
This will actually not work since if all hoppings are t the model is
not Hermitian. Do you mean a model with hopping t in one direction and the complex conjugate in the other?
Yes.It actually worked pretty well for a half filled case (Maybe for a wrong reason or it's by coincidence).
2.How does one adjust the input file for a site dependent parameters model?For example, I am interested in a 1D Hubbard model with 10- site chain for which the U term on the first 5 sites are different
from the remaining 5 sites (ie 1st 5 sites have U=U1 and the last 5 sites have U=U2) with a different hopping parameter linking the 2 sets of sites.What will change in the input file for such a site
dependent model?
You have to build a graph and not a lattice, and give different types to the various sites (vertices) and bonds (edges). You can then specify different t for the bonds and U for the sites.
Matthias
participants (2)
-
Akinlolu Akande
-
Matthias Troyer