TBit.Systems.KagomeLattice

Documentation

defaultParams :: Parameters

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

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.

kagomeAF :: Parameterized Hamiltonian

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.