Long-Range Hubbard DQMC

DQMC study of the 1D attractive Hubbard model with power-law long-range hopping:

$$t(r) = \frac{t}{r^\alpha}, \quad r = 1, \ldots, R_{\max}$$

Setting $R_{\max} = 1$ recovers standard nearest-neighbor hopping.

Research goal: map out the finite-temperature phase diagram in $(\alpha, T)$ space, and confirm the enhancement of pairing correlations ($\eta_P \to 0$) as $\alpha$ decreases.

---

Repository layout

lrHub/
├── simulation/
│   ├── hubbard_dqmc.jl       unified Julia DQMC engine (NN + LR)
│   └── run_simulation.py     SLURM submission script (argparse CLI)
├── analysis/
│   ├── __init__.py
│   └── extract.py            unified extraction module
├── notebooks/
│   ├── 00_sanity.ipynb       dispersion, DOS, density calibration
│   ├── 01_correlations.ipynb pair/Green's analysis, power-law fits
│   └── 02_phase_diagram.ipynb finite-T phase diagram (Step 4)
├── docs/                     reference PDFs (gitignored)
├── data/                     cluster output data (gitignored)
│   └── .gitkeep
└── results/                  selected figures (tracked, PDFs gitignored)
    └── .gitkeep

---

Quickstart

1. Local test (small parameters)

julia simulation/hubbard_dqmc.jl 1 -5 -2.2 15 16 2.0 1 100 200 10
# args:  sID U μ β L α Rmax N_burnin N_updates N_bins

2. Submit to cluster (NN, density calibration sweep)

python simulation/run_simulation.py \
    --U -5.0 --beta 40 --L 100 --alpha 2.0 --Rmax 1 \
    --sweep-mu -- -3.5 -3.0 -2.5 -2.0 -1.5 -1.0

3. Submit β sweep (after finding μ*)

python simulation/run_simulation.py \
    --U -5.0 --mu <mu_star> --L 100 --alpha 2.0 --Rmax 1 \
    --sweep-beta 40 60 80 100

4. LR α sweep

python simulation/run_simulation.py \
    --U -5.0 --mu <mu_lr_star> --beta 60 --L 100 --Rmax 50 \
    --sweep-alpha 0.5 0.8 1.0 1.5 2.0

---

Analysis

from analysis.extract import SimParams, extract_equal_time, scan_density_vs_mu

# Load pair correlator
params = SimParams(U=-5.0, mu=-2.4, beta=60.0, L=100, alpha=2.0, Rmax=1)
data = extract_equal_time(params, 'pair', 'position', base='/nfs/home/gissa/Hubbard')
r, P, err = data['r'], data['values'], data['errors']

# Density calibration scan
result = scan_density_vs_mu(U=-5.0, beta=40.0, L=100,
                            mu_range=[-3.5, -3.0, -2.5, -2.0],
                            alpha=2.0, Rmax=1)

Set the DATA_ROOT environment variable to avoid passing base= everywhere:

export DATA_ROOT=/nfs/home/gissa/Hubbard

---

Research roadmap

Step	Task	Notebook
1	Find μ* for n_σ = 0.4 (NN)	00_sanity.ipynb §4
2	NN simulations at n_σ = 0.4, β ∈ {40,60,80,100}	01_correlations.ipynb §1
3	LR simulations (fix Rmax, vary α) at n_σ = 0.4	01_correlations.ipynb §2
4	Finite-T phase diagram (η_P vs T for each α)	02_phase_diagram.ipynb

---

Dependencies

• Julia: SmoQyDQMC (includes LatticeUtilities, JDQMCFramework, JDQMCMeasurements)
• Python: numpy, matplotlib, scipy
• HPC: SLURM (for run_simulation.py)