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Workflows

The examples are organized by solver; this page shows how they fit together. Each step links to the folder whose README covers its options and pitfalls. Each block below starts in this examples/ directory.

Two checks follow every diagonalization, whatever the solver: its energy variance and PT2 say how far the saved state is from the exact one. Run them before using the state for anything else. The same driver, analysis/variance.py, handles every solver.

Note

These examples are tested against the upstream SBD commit pinned in vendor/sbd-upstream. With any other upstream revision, for example after git submodule update --remote, the functionality is not tested and may be broken.

Molecules: TPB or GDB

From an FCIDUMP and a determinant subspace.

# 1. diagonalize and save the state; note "Ground state energy:"
cd tpb       # from examples/
mpirun -np 4 python run_sbd_diag.py --adet_comm_size 2 --bdet_comm_size 2 \
    --bit_length 20 --tolerance 1e-8 --savename /path/to/h2o-

# 2. how far from exact: variance and PT2 (stochastic, on CPU)
cd ../analysis
mpirun -np 4 python variance.py --fcidump ../../vendor/sbd-upstream/data/h2o/fcidump.txt \
    --state /path/to/h2o- --bit_length 20 --energy <E from step 1>
  • Solve: tpb/ for an alpha × beta product subspace, including the SQD loops; gdb/ for an explicit determinant list, including heat-bath rounds that grow the subspace.
  • Check: analysis/.

Lattice and spin models: CAOP

From a Hamiltonian written as operator terms. After the ground state is checked, its Green's function gives the single-particle spectrum.

cd caop      # from examples/
# 0. a 2-site Hubbard model (t = 1, U = 4) and its half-filling basis; see caop/ for the format
printf '%s\n' -1 '-1.0 cdag 0 c 1' '-1.0 cdag 1 c 0' '-1.0 cdag 2 c 3' '-1.0 cdag 3 c 2' \
    '4.0 cdag 0 cdag 2 c 2 c 0' '4.0 cdag 1 cdag 3 c 3 c 1' > hub2.txt
printf '%s\n' 0101 0110 1001 1010 > hub2_basis.txt

# 1. the ground state, its basis split over 4 ranks and saved as 4 files, gs-000000.bin
#    to gs-000003.bin; note "Ground state energy:"
mpirun -np 4 python run_caop_diag.py --hamfile hub2.txt --basisfiles hub2_basis.txt \
    --system_size 4 --b_comm_size 4 --tolerance 1e-10 --savename gs-

# 2. how far from exact: variance and PT2, from the same files (--shards 4: the solve's
#    --b_comm_size). Here hub2_basis.txt is the whole half-filling sector, so both are
#    zero; over too small a basis, such as the two singly-occupied states 0110 and 1001
#    alone, the variance is large and E + PT2 recovers only part of the missing energy:
#    grow the basis
mpirun -np 4 python ../analysis/variance.py --hamfile hub2.txt --basisfiles hub2_basis.txt \
    --sites 4 --state gs- --shards 4 --bit_length 20 --energy <E0 from step 1>

# 3. the Green's function, over the N+1 sector (--wavefunction-shards 4, likewise)
printf '0111\n1011\n1101\n1110\n' > add_basis.txt
mpirun -np 4 python run_caop_spectrum.py --hamfile hub2.txt --sites 4 --loadname gs- \
    --wavefunction-shards 4 --reference-energy <E0 from step 1> --orbitals 0,2 \
    --channel addition --extra-detfile add_basis.txt --output add.csv

Each step here uses 4 ranks, one basis state each for this 4-state model; a larger basis spreads the same way over more ranks.

If the variance is large, the subspace is too small for the state to be trusted, for the Green's function as much as for the energy: grow it (more samples, or heat-bath expansion with --carryover_type 2), solve again, and check again.

The ground-state run, the check and the Green's function must agree on the run's settings, which the saved files do not record: --bit_length, the number of modes, the number of files (--b_comm_size of the solve), and --complex. A real/complex mismatch is refused.