This README gives a brief introduction to the MajoranaReps package.

The Majoranas

For the time being there are only 4 types of majoranas bx, by, bz and c, since the package was developed with the Kitaev Honeycomb Model in mind.

The vacuums is thus organised such that by(j)|0> == -i*bx(j)|0>, bz(j)|0> == -i*c(j)|0>. There transforamtions are applied automatically. This both of these lines will evaluate to true

im*bx(1)*Ket() == -by(1)*Ket()
im*c(1)*Ket() == -bz(1)*Ket()

Inner products

The package supports inner products through the constructions

IP = OpInnerProd(State1,State2)

IP = OpInnerProd(State1,Operator,State2)

The inner product automatically handles vector quantities. For instance, if one defines two different bases

Basis1 = [ bx(1)*Ket(), bx(2)*Ket(), bx(3)*Ket(),bx(1)*bx(2)*bx(3)*Ket()]
Basis2 = [ by(1)*Ket(), by(2)*Ket(), by(3)*Ket(),by(1)*by(2)*by(3)*Ket()]

and then apply OpInnerProd(Basis1,Basis2) one will as a result get the 4x4 array

4×4 Array{Complex{Int64},2}:
 0-1im  0+0im  0+0im  0+0im
 0+0im  0-1im  0+0im  0+0im
 0+0im  0+0im  0-1im  0+0im
 0+0im  0+0im  0+0im  0+1im

MathLink

The package also supports the use of MathLink and MathLinkExtras syntax for algebraic prefactors. This allows for constructions like W"a"*bx(1) or W`-I b`*by(1)

NB: MathLink needs to be loaded before invoking MajoranaReps the first time.