Tutorials

Some tutorials.

• Brinkman-Rice metal-insulator transition
  • The model
  • Construct the non-interacting terms \(\hat{H}^{0}\)
  • Local structure on a site
  • Construct the interactions \(\hat{H}_i^{\mathrm{int}}\)
  • Enforce paramagnetism
  • Setup the k-space integral calculator
  • Setup the solvers and find a self-consistent solution
  • Observables on a site
  • Exercises
  • Conclusion
  • Bonus
• Multiple clusters on the kagome lattice
  • The model
  • Construct a matrix of the dispersion relations
• Constructing the RISB self-consistent loop
  • Example model: bilayer Hubbard
  • A: Construct \(\hat{H}_0^{\mathrm{kin}}\)
  • B: Construct \(\hat{H}_i^{\mathrm{loc}}\)
  • C: Construct \(\hat{H}^{\mathrm{qp}}\)
  • D: Setup k-integrator function
  • E: Setup mean-field matrices
    • Helper functions
  • F: Solving \(\hat{H}^{\mathrm{emb}}\)
  • G: Closing the loop
  • Exercises
  • Conclusion
  • Skeleton code cheat sheet