Schwinger Model Simulation

This repo simulates U(1) gauge theory on a 1+1 D lattice with 2 mass degenerate fermions.

The analysis code includes:

• Automatic wick contractions
• Distillation
• GEVP
• Theta term reweighting

Quick Start

See example.ipynb for how to construct arbitatry interpolator bases for GEVP and how to analyze configurations.

Map of the repo (in progress):

• SchwingerModel.py: contains the gauge generation code
  • SchwingerModel class
    • parameters:
      • dimx, dimt: spacial and temporal extent of the lattice
      • metroSteps: the number of metropolis-hastings steps
      • beta: coupling constant, proportional to $e^{-2}$
      • fMass: mass of the fermion
      • aSpacing: relates to the spacing between the grid points
      • cgRtol: relative tolerance for the cg solves
      • numSubSteps: number of molecular dynamics steps for each HMC iteration
      • randSeed: random seed for numpy rng
      • tunneling: whether to propose changing the topological charge after each HMC iteration
• analysis.py: contains some simple analysis functions, often superseeded elsewhere
  • plaqStats
    • returns the average and std. err. of the plaquette
  • correlStats
    • returns the correlator between two fermion bilinears of Gamma
    • can include the disconnected part
    • jacobi smearing can be added using the smearing argument along with kappa and smearingSteps
    • projection to definite momentum $k \in \mathbb{Z}$
  • effectiveMassStats
    • does the same thing as correlStats, but returns the effective mass instead
    • if data is noisy, then this works poorly because effective mass can become NaN in boostrap draws
  • effectiveMassProp
    • takes the output of correlStats and returns the effective mass, with errors propagated
    • used because of effectiveMassStats problems, but error bars are larger than they should be
  • numDensityStats
    • finds the expected value of the number density with errors given an chemical potential
    • numberDensity is found by reweighting the configutions that we generated with zero chemical potential
    • may not be correct for the theory we are trying to analyze (i.e. reweighting here might be wrong)
  • getCorrelation
    • used by correlStats to find the correlation function for one gauge configuration
  • get_integrated_autocorr_time_statistical
    • given a rho_bar and number of configurations find the corresponding integrated autocorrelation time
    • rho_bar can be generated by funcitons like getNumDensityRhoBar and getEffMassRhoBar