Hi Matthias

I just choose a zero chemical-potential; is a non-zero value required to extract the correct t/U dependence?

When I chose Nmax = 2, I want the 2x1 cluster to have totally 2 bosons over the 2 sites, with a maximum of 2 bosons per site i.e. 3 Fock-eigenstates: 02, 11, 20. Is my interpretation of Nmax correct?

Thanks, Vipin

On Fri, 19 Feb 2010, Matthias Troyer wrote:

Hi Vipin,

How do you choose your chemical potential? Note that in the parameter file below you dud not fix the number of particles. DId you want the number of particles fixed to 2?

Matthias

On 19 Feb 2010, at 07:01, Vipin Varma wrote:

...

Hi

I am trying the Lanczos method for solving the Bose-Hubbard model on a square lattice, to get the t/U dependence of the ground state energy per site. I tried a simple 2x1 cluster with open and periodic boundary conditions and I get a linear dependence for the energy on t/U; analytically (which I am reasonably sure is correct), I get a parabolic dependence for the energy on t/U, if I consider 2 bosons over 2 sites.

Here is my parameter file:

///////////////////////////

LATTICE_LIBRARY="../lattices.xml"; LATTICE="square lattice";

MODEL_LIBRARY="../models.xml"; MODEL="boson Hubbard"; U = 1; Nmax = 2; L=2; W =1; {t=0.1;} {t=0.01;} {t=0.02;} {t=0.03;} {t=0.04;} {t=0.05;} {t=0.06;} {t=0.07;} {t=0.08;} {t=0.09;}

///////////////////

I have tried Nmax = 2,4,6, but all give me a linear dependence; also strangely, the energy range does not change much when I vary the value of U by orders of magnitude.

I guess I am missing something simple. Any ideas will be appreciated.

Vipin

Hi Matthias

Thanks, now I am getting the right plots.

Vipin

On Fri, 19 Feb 2010, Matthias Troyer wrote:

Hi Vipin,

On 19 Feb 2010, at 07:36, Vipin Varma wrote:

...

Hi Matthias

I just choose a zero chemical-potential; is a non-zero value required to extract the correct t/U dependence?

When I chose Nmax = 2, I want the 2x1 cluster to have totally 2 bosons over the 2 sites, with a maximum of 2 bosons per site i.e. 3 Fock-eigenstates: 02, 11, 20. Is my interpretation of Nmax correct?

You indeed have a maximum of 2 bosons per site, but do not fix the total number. Hence you have the following Hilbert space:

00, 01, 10, 11, 20, 02, 21, 12, 22

To fix the number of particles in the ED codes you need to set CONSERVED_QUANTUMNUMBERS="N" and N_total=2, otherwise you will work in a grand canonical ensemble with mu=0. The QMC codes always work in the grand canonical ensemble.

Matthias