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.