Solution of Bose Hubbard model using ARPACK

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Sayan Lahiri
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Sir currently I am trying to solve a system which has 8 sites and each site can have 3 possible states(0 or 1 or 2).So the dimension of matrix is 6561*6561.The lapack works good till 3000*3000.But for larger system it fails.I have studied the dsdrv1.f example from arpack where they have solved the problem for central difference discretization of the 2-dimensional Laplacian on the unit square [0,1]x[0,1] with zero Dirichlet boundary condition.But I can not understand what changes i should make in my case.Please help
 

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I can not understand how to apply the example given in arpack
 
Can you give more details of what you are trying to do and what you have tried?