# Comp. GS of hubbard hamiltonian

1. Sep 13, 2010

### babylonia

Hi,

I'm trying to repeat the numerical calculation of D Jaksch's article PRL 81,3108.
It is about using variational method for the ground state of bose hubbard hamiltonian:
H=-J\sum{a+i+1ai}+U\sum{nini},where i denotes the lattice index
the trial function is based on Gutzwiller ansatz:
G=\prodi{\summ=0toInffim|m>i, where m denotes the number of atoms in a certain lattice, fim is the variational parameter,
What should be done is to minimize
<G|H|G>-mu <G|\sum {ni}|G>, where mu is the given chemical potential.
As I see it, this is done by inserting G, and should lead to a set of nonlinear equations, solve it will give the solution of variational parameter.
However, I am having trouble how to solve it. since fimis complex, and they must satisfy normalization condition, the resulting nonlinear equations seem difficult.

This is really a big problem for me. if any tips on such problem, I'd appreciated it

Last edited: Sep 13, 2010