HPhi Stuck at ‘Calculate HilbertNum for fixed Sz’ for Large Hilbert Space”

[del2341]

Hello, Recently, I have been using HPhi to perform exact diagonalization calculations for the energy spectrum of the Kagome lattice. I am running the calculation on a machine with 1 TB of memory. I constructed a sparse Hamiltonian with a Hilbert space dimension of 1,026,675, and attempted to solve for the ground state energy using the CG method.

However, the program gets stuck at the line:
“Start: Calculate HilbertNum for fixed Sz.”
It has been in this state for two days without any progress. In addition to the CG method, I also tried the Lanczos method, but encountered the same issue — the program still hangs at the same point.

Given the Hilbert space size and the available memory, I don’t think it’s a memory issue. The number of non-zero elements should also be well below any Int32 limit. Do you have any idea why the calculation cannot proceed?

Here is my input configuration:

W = 9
L = 3
model = "FermionHubbard"
method = "CG"
lattice = "triangular"
t = 1.0
U = 4.0
nelec = 28
2Sz = 22

Could you please take a look? Thank you very much in advance.

[tmisawa]

@del2341

Thank you for your message. I have checked the issue, and it seems that the delay is caused by the loop generating the Hilbert space. Although the final dimension of the Hilbert space itself is not very large, the generation process involves a long loop that iterates up to 2^27 (=134,217,728), which results in significant computational time.
Therefore, it is not a bug.

I am currently considering whether it is possible to speed this up by changing the algorithm.
I would appreciate it if you could allow me a little more time.

[tmisawa]

@del2341

I have added a new function called omp_sz_hacker_ForLargeSystems in branch LargeHilbertSpace.
This function avoids looping over all 2^{Ns} states and instead extracts only the states with a specified Sz.

By setting CalcHS 2 in modpara.def, you can enable this function.

I have confirmed that with the input file you specified (stan.in),
the Hilbert space can be generated within one minute,
and the calculation completes successfully.
Also, in the range I have tested, the function appears to work correctly.
However, please let me know if you encounter any issues.

Note that this algorithm is currently not parallelized with OpenMP,
as implementing OpenMP parallelization here is somewhat difficult.
While it should not be a problem for Hilbert spaces up to around 10^5 in size (as they complete in under a minute),
please be cautious when handling larger Hilbert spaces.

If you have any questions or run into any problems, feel free to ask.

[del2341]

Thank you for your reply. After using that function, I was indeed able to obtain the energy successfully.

I have another question. It appears that the current version of HPhi only supports basis sizes that fit within a 32-bit integer. Is there any way to continue calculations when the whole Hilbert-space dimension exceeds the Int32 limit? For example, consider the following setup. The final dimension is just 45:

W = 15
L = 3
model = "FermionHubbard"
method = "CG"
lattice = "triangular"
t = 1.0
U = 4.0
nelec = 46
2Sz = 44

Any guidance would be greatly appreciated.

[ultimatile]

To prevent information contamination, please open a new issue for any other question or problem.