check shell conditions of tight binding models

• Check open or closed shell for each system (closed shell recommended for QMC)

• Lattices

  • 1D
    • Chain: E(k) = -2cos(k)
  • 2D
    • Square: E(kx,ky) = -2(cos(kx)+cos(ky))
    • Triangular: E(kx,ky) = -2(cos(kx)+cos(ky)+cos(kx+ky))
    • Honeycomb: E_{1,2}(kx,ky) = \pm |1 + exp(-i kx) + exp(-i ky)|
    • Kagome: E_{1,2,3}(kx,ky) = 2, -1 \pm \sqrt(1 + 8 cos(kx/2) cos(ky/2) cos((kx-ky)/2))

• Boundary

  • 1D
    • Periodic (P)
    • Antiperiodic (AP)
  • 2D
    • P-P
    • P-AP
    • AP-P
    • AP-AP

• In data files,

  • "Energy density" = E/Nsite/Nspin
  • "Number of electrons" = number of up spins = number of down spins

• Results (DOS)

  • Chain
    

  • Square
    

  • Triangular
    

  • Honeycomb
    

  • Kagome
    

• References

  • https://arxiv.org/abs/2008.05544