6.4. Memory Management

This section describes how \({\mathcal H}\Phi\) manages memory for large-scale calculations.

6.4.1. Memory Requirements

The dominant memory usage in \({\mathcal H}\Phi\) comes from storing the state vectors. For a Hilbert space of dimension \(D\) distributed across \(P\) MPI processes, each process requires:

Lanczos method

  • Two state vectors (v0, v1): \(2 \times D/P \times 16\) bytes (complex double)

  • One buffer for MPI communication: \(D/P \times 16\) bytes

LOBPCG method

  • Multiple state vectors for subspace iteration

  • Buffer for orthogonalization

List arrays

  • list_1: \(D/P \times 8\) bytes (unsigned long)

  • list_2_1, list_2_2: depends on system size

6.4.2. Memory Allocation

\({\mathcal H}\Phi\) allocates memory dynamically using wrapper functions defined in common/setmemory.c. These functions handle allocation for various data types:

  • d_1d_allocate: 1D double array

  • cd_1d_allocate: 1D complex double array

  • i_2d_allocate: 2D integer array

  • lui_1d_allocate: 1D unsigned long integer array

Memory is allocated at the beginning of the calculation in xsetmem.c and freed at the end.

6.4.3. Estimating Memory Usage

Before running a calculation, you can estimate the required memory:

(6.5)\[M_{\text{total}} \approx \frac{D}{P} \times (N_v \times 16 + N_l \times 8) \text{ bytes}\]

where:

  • \(D\) is the Hilbert space dimension

  • \(P\) is the number of MPI processes

  • \(N_v\) is the number of state vectors (typically 3-4 for Lanczos)

  • \(N_l\) is the number of list arrays (typically 1-3)

Example

For a 16-site Hubbard model with 4 up and 4 down electrons (\(S_z = 0\)):

  • Hilbert space: \(D = \binom{16}{4}^2 = 1,820^2 = 3,312,400\)

  • With 4 MPI processes: \(D/P = 828,100\) states per process

  • Memory per process: approximately 50 MB for state vectors

6.4.4. Memory Optimization Strategies

Increasing MPI processes

Distributing the Hilbert space across more processes reduces per-process memory requirements.

Using symmetries

Particle number conservation, \(S_z\) conservation, and other symmetries reduce the Hilbert space dimension.

Restart functionality

For very large calculations, the restart feature allows breaking the calculation into smaller chunks.

6.4.5. Common Memory Issues

Out-of-memory errors

If the calculation runs out of memory, try:

  1. Increase the number of MPI processes

  2. Use symmetry restrictions

  3. Request more memory per node on cluster systems

Memory leaks

\({\mathcal H}\Phi\) carefully manages memory to avoid leaks. If you observe growing memory usage, please report it as a bug.