TBit-0.4.2.3: Utilities for condensed matter physics tight binding calculations.

TBit.Systems.KagomeLattice

Synopsis

# Documentation

The default set of scalar parameters is:

• "t" = 1, the hopping parameter
• "tSO" = 1, the intrinsic spin-orbit coupling
• J = 1, the Heisenberg exchange parameter

The default vector parameters are the d-orbital local moments on the three sites. Each of them takes the form: (-cos theta, -sin theta, 0) where theta is:

• "d0" : theta = pi/2
• "d1" : theta = pi2 + 2pi3
• "d2" : theta = pi2 + 4pi3

These can be changed by using `parameters` to set all of them explicitly.

parameters :: [(String, Complex Double)] -> [(String, Vector (Complex Double))] -> Parameters Source

Set the named parameters to their given complex values. This function is used to implement `defaultParams` as

```defaultParams = parameters [ ("t"  , 1.0 :+ 0.0)
, ("tSO", 0.2 :+ 0.0)
, ("J" ,  1.7 :+ 0.0) ]
[ ("d0" , n21 )
, ("d1" , n02 )
, ("d2" , n10 ) ]
where n10 = negate \$ fromList [ cos ang01 , sin ang01 , 0.0 ]
n21 = negate \$ fromList [ cos ang12 , sin ang12 , 0.0 ]
n02 = negate \$ fromList [ cos ang20 , sin ang20 , 0.0 ]
ang01 = pi/2.0 + 4.0*pi/3.0
ang12 = pi/2.0
ang20 = pi/2.0 + 2.0*pi/3.0```

but you can use it to generate your own parameter list. For more advanced manipulation, like setting the mesh size or the primitive lattice vectors, you'll have to constuct a `Parameters` type explicitly.

The kagomé hamiltonian provided here includes nearest-neighbor hopping, noncollinear AF order due to localized d-orbital moments, and spin-orbit coupling which breaks mirror symmetry.