Solution of Bose Hubbard model using ARPACK

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SUMMARY

The discussion focuses on solving the Bose Hubbard model using ARPACK for a system with 8 sites, each having 3 possible states, resulting in a matrix dimension of 6561x6561. The user reports that LAPACK functions efficiently handle matrices up to 3000x3000 but fails for larger dimensions. They reference the dsdrv1.f example from ARPACK, which demonstrates solving the 2-dimensional Laplacian with zero Dirichlet boundary conditions, but seek guidance on adapting this example to their specific problem.

PREREQUISITES
  • Understanding of the Bose Hubbard model
  • Familiarity with ARPACK and its dsdrv1.f example
  • Knowledge of LAPACK and its limitations
  • Basic concepts of finite difference methods and boundary conditions
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  • Study ARPACK documentation for advanced usage and matrix size handling
  • Explore LAPACK alternatives for large matrix computations
  • Research finite difference methods specific to the Bose Hubbard model
  • Learn about efficient matrix storage techniques for high-dimensional systems
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Researchers and practitioners in quantum physics, computational physics, and numerical analysis, particularly those working on the Bose Hubbard model and large matrix computations.

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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