- #1
babylonia
- 11
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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
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
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