Solution of Bose Hubbard model using ARPACK

In summary, the conversation is about the difficulty in solving a system with 8 sites and 3 possible states for each site, resulting in a large matrix size of 6561*6561. The lapack algorithm works well for smaller systems, but fails for larger ones. The person has looked at an example from arpack, but is unsure of how to apply it to their problem. They are asking for more details and guidance on how to proceed.
  • #1
Sayan Lahiri
2
0
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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  • #2
I can not understand how to apply the example given in arpack
 
  • #3
Can you give more details of what you are trying to do and what you have tried?
 

Related to Solution of Bose Hubbard model using ARPACK

1. What is the Bose Hubbard model?

The Bose Hubbard model is a theoretical model used to describe the behavior of a system of interacting bosons (particles with integer spin) in a lattice. It takes into account the effects of both on-site interactions between particles and hopping between lattice sites.

2. What is ARPACK?

ARPACK (ARnoldi PACKage) is a software library used for solving large-scale eigenvalue problems. It uses the Arnoldi algorithm to compute a small number of eigenvalues and corresponding eigenvectors of a sparse matrix.

3. How is ARPACK used to solve the Bose Hubbard model?

ARPACK is used to solve the Bose Hubbard model by first discretizing the model into a sparse matrix. This matrix is then passed to ARPACK, which uses its algorithms to compute the eigenvalues and eigenvectors of the matrix. These results provide information about the energy levels and corresponding wave functions of the system.

4. What are the advantages of using ARPACK for the Bose Hubbard model?

ARPACK is advantageous for solving the Bose Hubbard model because it can efficiently handle large-scale eigenvalue problems, which are difficult to solve using traditional methods. It also allows for the calculation of a small number of eigenvalues and eigenvectors, which is sufficient for most practical purposes.

5. Are there any limitations to using ARPACK for the Bose Hubbard model?

One limitation of using ARPACK for the Bose Hubbard model is that it assumes the system is in thermal equilibrium. This may not accurately represent the behavior of the system in non-equilibrium situations. Additionally, ARPACK may struggle with highly degenerate systems or those with complex energy landscapes.

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