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Nov 22nd, 2017
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  1. function InfiniteHamil(E, EA, EAB, FA_list, FB_list, d_list, ϵ_list)
  2. #------------------------------
  3. num_steps = 200
  4. x_values = collect(0:1/num_steps:1)
  5. y_values = []
  6.  
  7. #------------------------------
  8. for x in x_values
  9. k = path(x)
  10. z1 = exp(im*k[1])
  11. z2 = exp(im*k[1]/2)*exp(im*sqrt(3)*k[2]/2)
  12. c1 = cos(k[1])
  13. c2 = cos(k[1]/2 + k[2]*sqrt(3)/2)
  14. c12 = cos(k[1]/2 - k[2]*sqrt(3)/2)
  15.  
  16. secondHam = vcat( hcat(E+ 2*(c1*d_list[1] + c2*d_list[2]+ c12*d_list[5]),
  17. FA_list[1]+ conj(z2)*(FA_list[2]+z1*FA_list[3]),
  18. FB_list[1]+ conj(z2)*(FB_list[2]+z1*FB_list[3])),
  19. hcat((FA_list[1]+ conj(z2)*(FA_list[2]+z1*FA_list[3]))',
  20. EA+ 2*( c1*ϵ_list[1]+c2*ϵ_list[2]+c12*ϵ_list[5]),
  21. EAB ),
  22. hcat((FB_list[1]+ conj(z2)*(FB_list[2]+z1*FB_list[3]))',
  23. EAB',
  24. EA+ 2*( c1*ϵ_list[1]+c2*ϵ_list[2]+c12*ϵ_list[5]) ))
  25.  
  26.  
  27. println(typeof(E+ 2*(c1*d_list[1] + c2*d_list[2]+ c12*d_list[5])))
  28. println(typeof(FA_list[1]+ conj(z2)*(FA_list[2]+z1*FA_list[3])))
  29. println(typeof(FB_list[1]+ conj(z2)*(FB_list[2]+z1*FB_list[3])))
  30. println(typeof((FA_list[1]+ conj(z2)*(FA_list[2]+z1*FA_list[3]))'))
  31. println(typeof(EA+ 2*( c1*ϵ_list[1]+c2*ϵ_list[2]+c12*ϵ_list[5])))
  32. println(typeof(EAB ))
  33. println(typeof((FB_list[1]+ conj(z2)*(FB_list[2]+z1*FB_list[3]))'))
  34. println(typeof(EAB' ))
  35. println(typeof(EA+ 2*( c1*ϵ_list[1]+c2*ϵ_list[2]+c12*ϵ_list[5])))
  36. println(typeof(secondHam))
  37.  
  38. push!(y_values , filter(x -> x > -10, sort(real(eigvals(secondHam))) ))
  39.  
  40. end
  41. #------------------------------
  42. y_values = hcat(y_values...)
  43. plotData(x_values,y_values)
  44. end
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