Solution of Bose Hubbard model using ARPACK

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The discussion revolves around solving a complex system involving 8 sites, each with 3 possible states, resulting in a large matrix of dimensions 6561x6561. The user is facing challenges with LAPACK, which performs well for matrices up to 3000x3000 but fails for larger sizes. They reference an example from ARPACK that addresses the central difference discretization of the 2-dimensional Laplacian with specific boundary conditions but are struggling to adapt the methodology to their own problem. The user seeks clarification on how to implement the ARPACK example effectively for their system.
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?
 

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