SOM

Official Resources

• Homepage: https://github.com/kcd2015/SOM
• Documentation: https://github.com/kcd2015/SOM
• Source Repository: https://github.com/kcd2015/SOM
• License: Open Source (GPL or similar)

Overview

SOM (Stochastic Optimization Method) is a code for the analytic continuation of quantum Monte Carlo (QMC) data. It solves the inverse problem of reconstructing real-frequency spectral functions from imaginary-time or Matsubara frequency Green's functions. It implements a stochastic optimization approach, as proposed by Mishchenko et al., often providing a robust alternative to Maximum Entropy (MaxEnt) by avoiding entropic regularization bias.

Scientific domain: Analytic Continuation, Condensed Matter Physics, Numerical Methods Target user community: DMFT/QMC practitioners needing spectral functions

Theoretical Methods

• Stochastic Optimization (Mishchenko's method)
• Analytic Continuation
• Inverse Ill-posed Problems
• Green's function inversion
• Fredholm integral equation of the first kind

Capabilities (CRITICAL)

• Reconstruction: Recovers Real-frequency spectral function $A(\omega)$ from $G(\tau)$ or $G(i\omega_n)$ input data.
• Alternative to MaxEnt: Does not rely on entropic regularization, potentially offering different handling of sharp features.
• Error Estimation: Can provide estimates of reliability for reconstructed features.
• Sampling: Uses Monte Carlo sampling of the solution space (rectangles configuration).

Key Features

TRIQS Integration:

• Often developed within or compatible with the TRIQS ecosystem.
• Designed to handle noisy QMC data effectively.

Configurable Updates:

• Elementary updates include shifting, resizing, adding, removing, splitting, and gluing rectangles to form the spectrum.

Inputs & Outputs

• Input formats:
  • QMC Data: Green's function data (tau or Matsubara).
  • Error bars (covariance matrix).
  • Parameter file defining MC steps, updates, and deviation function.
• Output data types:
  • Real-frequency spectral function $A(\omega)$.

Workflow and Usage

Used as a post-processing step after a QMC/DMFT calculation.

1. Load QMC data ($G(\tau)$).
2. Configure stochastic parameters.
3. Run SOM to stochastically sample the space of possible spectra.
4. Average samples to obtain final $A(\omega)$.

Comparison with Other Codes

Verification & Sources

Primary sources:

1. GitHub Repository: https://github.com/kcd2015/SOM
2. Literature: Mishchenko et al., "Stochastic optimization method for analytic continuation..." (arXiv/Phys. Rev. B).

Verification status: ✅ VERIFIED

• Source code: OPEN (GitHub)
• Method: Established stochastic continuation technique (Mishchenko)