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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+1}a_{i}}+U\sum{n_{i}n_{i}},where i denotes the lattice index

the trial function is based on Gutzwiller ansatz:

G=\prod_{i}{\sum_{m=0toInf}f^{i}_{m}|m>_{i}, where m denotes the number of atoms in a certain lattice, f^{i}_{m}is the variational parameter,

What should be done is to minimize

<G|H|G>-mu <G|\sum {n_{i}}|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 f^{i}_{m}is 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

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# Comp. GS of hubbard hamiltonian

Can you offer guidance or do you also need help?

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