morec: MOR+EC reduced-order impurity solver

Reduced-order models of single-particle Green’s functions that combine eigenvector continuation (EC) in parameter space with model order reduction (MOR) in frequency, applied as an impurity solver for dynamical mean-field theory (DMFT) on the Bethe lattice. This is the code behind Compact representation of strongly correlated Green’s functions: the MOR+EC way to explore phase space (N. Hogan, A. F. Kemper, C. Mejuto-Zaera), arXiv:2609.28647.

Install

pip install -e .              # numpy, scipy, psutil
pip install -e ".[paper]"     # + matplotlib, to regenerate the figures
pip install -e ".[test]"      # + pytest

Quick start

from morec import BuildConfig, DMFTConfig, EnrichConfig, MORSolver, build, sweep, sweep_values

# Offline stage: greedy EC basis over a Sobol grid, then MOR projections at r frequencies.
build(BuildConfig(N=8, NI=2, r=3, ec_tol=1e-2, bw_lo=[1.0, 0.01], bw_hi=[1.0, 0.75]), "atlas")

# Online stage (optional): a coarse DMFT sweep that enriches the ROM where it is inaccurate.
cfg = DMFTConfig(N=8, NI=2, bw_ratios=[1.0, 0.1])
solver = MORSolver("atlas", bw_ratios=cfg.bw_ratios, enrich=EnrichConfig(variance_tol=1e-4))
sweep(cfg, solver, "runs/coarse", sweep_values(0, 10, 1, clamp_min=0.01), bwr_vals=sweep_values(0.1, 0.5, 0.1))

# Fine scan entirely inside the ROM.
solver = MORSolver("atlas", bw_ratios=cfg.bw_ratios)
sweep(cfg, solver, "runs/fine", sweep_values(0, 8, 0.1, clamp_min=0.01), bwr_vals=sweep_values(0.1, 0.5, 0.01))

The same from the command line:

morec build atlas --N 8 --NI 2 --r 3 --ec_tol 1e-2 --bw_lo 1 0.01 --bw_hi 1 0.75
morec dmft runs/coarse --N 8 --NI 2 --bw_ratios 1 0.1 --atlas atlas --U 0 10 1 --bwr 0.1 0.5 0.1 --enrich
morec dmft runs/fine --N 8 --NI 2 --bw_ratios 1 0.1 --atlas atlas --U 0 8 0.1 --bwr 0.1 0.5 0.01
morec dmft runs/ed --N 8 --NI 2 --bw_ratios 1 0.1 --solver ED --U 0 10 1 --bwr 0.1 0.5 0.1

Axis options take one value or lo hi step; --mu sets an absolute chemical potential (default half filling), --JU a Hund coupling proportional to U. Every sweep point is written to <outdir>/[bwr*/]J*/U*/[mu*/] (dmft_log.txt, dmft_metadata.json, gf_sigma_current.npz, bath_history.npz); interrupted sweeps resume where they stopped.

How the code maps onto the method

An atlas directory holds atlas.json and one directory per patch (meta.json, the EC basis B.npz, projected terms h_r.npz, per orbital pair pair_i_j.npz, and the projectors V_p_i_j.npz/V_h_i_j.npz, which are only needed for enrichment). B and V are stored as scipy.sparse matrices. Online enrichment rewrites the atlas in place, so work on a copy; it appends the new projector columns as extra files (V_p_i_j.addNNNNNN.npz), which are read together with the base file up to the column count recorded in meta.json.

Reproducing the paper

cd paper
python make_figures.py          # Figs. 4-11 and Table I from paper/data (2 MB) -> paper/figures/

paper/data was reduced from the production runs by extract_data.py --layout production. To regenerate everything from scratch, run the campaigns and extract again:

export MOREC_RUNS=/scratch/runs
python campaigns/run_campaign.py n8ni2 build     # Figs. 6, 9, 10, 11, Table I
python campaigns/run_campaign.py n8ni2 enrich
python campaigns/run_campaign.py n8ni2 post
python campaigns/run_campaign.py n8ni2 ed
python campaigns/run_campaign.py n10ni1 ...      # Figs. 7, 8 (same steps)
python campaigns/run_campaign.py siam_demo build # Fig. 5
python paper/extract_data.py --raw $MOREC_RUNS --layout campaign fig5 fig6_compute fig6 fig7_8 fig9 fig10 fig11

Figs. 1-3 are drawings and are not generated. finite_j (campaign and figures) covers the finite-Hund’s-coupling runs that are not part of the paper. Exact figure reproduction needs matplotlib 3.10 (pinned in the paper extra; later versions choose different log-axis ticks) and latex on the PATH (otherwise the text falls back to matplotlib’s fonts).

Notes and limitations

• Timings: ED and the ROM evaluate their Green’s functions with the same Lanczos recursion (lanczos.haydock_gf), so per-call times compare like with like. The ROM’s gain is mostly in the ground state and grows with the size of the impurity model.
• Bath pole order: bath sites are interchangeable, but a reordered bath is a different parameter point for the reduced model. Every bath is therefore brought to one order (each side of zero in ascending |energy|, bath.canonical_bath) before ED or the ROM uses it, offline and online, and the doped bath fit returns its poles in that order. Results for models with one free pole per side (the paper’s N=8, NI=2 runs) are unaffected. Atlases built before this was added remain usable but were trained and enriched on unordered baths.
• Patch.compress (a second projection of the ROM onto the directions used at a given set of parameter points) is experimental and is not used in the paper.
• Multi-patch atlases (n_patches_*, k_local, halo) and off-diagonal G_ij are carried over from development and have not been validated; using them emits a warning. For the models here (no inter-orbital hopping) G_ij vanishes for i != j, so off-diagonal pairs are dropped. The solvers and the DMFT loop assume an orbital-diagonal G; AIM warns if a term added to it couples the orbitals.

License

MIT, see LICENSE.