Types and standard operation for k grids and tight binding dispersions in solid state theory. This project is inteded to be used as a backend for k grid related operations in order to abstract over the actual k grid logic. For an example usage see LadderDGA.jl and jED.jl

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Available Tight Binding Models

KGrid are generated as follows:

Nk = 100 # Number of k-sampling points
GS = "..." # Grid-string, see below

• GS = "2Dsc-t-tp-tpp": 2D simple cubic with t, t', t''. For slightly improved performance, one can ommit t' and t'' when not needed, i.e. Nk = 100; kG = gen_kGrid("2Dsc-1.1", Nk)
• GS = "3Dsc-t-tp-tpp": 3D simple cubic
• GS = "4Dsc-t-tp-tpp": 4D simple cubic
• GS = "fcc-t": fcc, t' and t''must be left out!
• GS = "bcc-t": bcc, t' and t''must be left out!
• Hofstadter:P:Q-t-tpt-pp: Hofstadter model with P,Q parameters for magnetic field and hopping t, t', t''

Interface

• kG = genKGrid(s, nk) will generate a k grid with nk points in each direction from a configuration string. Examples are s = "2Dsc-1.0" (2D simple cubic with hopping parameter - t = 1.0), s = "FCC-1.0-1.1-1.3" for a FCC lattice.

• gridshape(kG) returns the shape of a k grid. Example: (4,4) for a lattice generated with genKGrid("2Dsc-1.0", 4)

• Nk(kG) returns the number of k points for the given grid. Example: 16 for a lattice generated with genKGrid("2Dsc-1.0", 4)

• gridPoints(kG) returns the k vektors for the given grid.

• dispersion(kG) returns the dispersion relation, i.e. an array of energy value for each point of gridPoints(kG).

• grid_type(kG) returns the KGridType of the given grid without the dimension the grid lives on.

• conv(kG, arr1, arr2) returns the convolution of the arrays arr1 and arr2 (any function evaluated on kG) on kG. This is usefull for the evaluation of expressions like G(q) = sum_k G(q)*G(k+q)

• conv_fft(kG, arr1, arr2) and conv_fft1(kG, arr1, arr2) are helpers, used when arr1 or both arr1 and arr2 are already fourier transformed (used for repeated evaluation with the same kernel).