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:
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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;}
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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