Tuning and Best Practices

Practical advice on choosing simulation parameters for reliable and efficient ALF runs.

Philosophy¶

The formal documentation (PDF) derives the algorithms. This section focuses on what to set, what to look for, and what can go wrong — practical knowledge that comes from experience running simulations.

Each sub-page follows a consistent format:

1. Parameters — name, where it’s set, typical range

2. Guidelines — how to choose good values, what to monitor

3. Model-specific notes — when defaults don’t apply

4. Known pitfalls — common mistakes and their symptoms

Topics¶

The first two topics apply to every ALF simulation. HMC and Tempering are relevant only when using those specific update schemes.

[[Discretization]]¶

The imaginary-time step Dtau controls the Trotter decomposition error. Too large and results are biased; too small and the simulation is unnecessarily expensive. Guidance on choosing Dtau and extrapolating to the continuous-time limit.

[[Stabilization Parameters]]¶

Choosing Nwrap (the number of imaginary-time slices between QR stabilizations) and selecting a stabilization scheme (STAB1/STAB2/STAB3/LOG). Getting this wrong leads to numerical instability or wasted computation.

[[HMC Parameters]]¶

Tuning the Hybrid Monte Carlo updating scheme: leap-frog step size (Delta_t_Langevin_HMC), number of integration steps (Leapfrog_Steps), the mass matrix preconditioner (Apply_B_HMC), and how many HMC trajectories to run between sequential sweeps (N_HMC_sweeps).

[[Tempering]]¶

Parallel tempering configuration: how to choose the temperature grid, how many replicas to use, and what exchange acceptance rates to target.

General Advice¶

• Always check the info file after a run. It reports acceptance rates, precision of the Green’s function, and walltime. Anomalous values are the first sign of trouble.

• Start small. Test parameter choices on small lattices (e.g. 4×4) before committing to expensive production runs. The physics should be qualitatively the same.

• Compare with exact results when possible. Small systems (e.g. 2-site or 4-site Hubbard) have exact diagonalization results. Use them to validate your setup.

• Monitor autocorrelation. If consecutive bins are correlated, increase NSweep (sweeps per bin) or use rebinning in the analysis step.

• Start with sequential updates. The default sequential (single-site) updating scheme is the safest starting point. Switch to HMC or Langevin only if needed — e.g., to overcome or reduce autocorrelation issues. When using HMC, keep sequential updates enabled alongside it (Sequential = .true.) for ergodicity. Note that Langevin dynamics currently cannot be combined with sequential updates; Metropolis-adjusted Langevin (MALA) moves are planned for a future release.