Julia package for the implementation of q-deformed Wigner Symbols. Additionally, this provides an extension to TensorKit.jl for working with tensors that have q-deformed SU(2) symmetry.
Currently, the package provides the following exported functions that define q-analogs:
-
q_number(n::Integer, q::Number):$[n]_q = \frac{1 - q^n}{1 - q}$ -
q_factorial(n::Integer, q::Number):$[n]_q! = \prod [k]_q$ -
q_binomial(n::Integer, k::Integer, q::Number):$\binom{n}{k}_q = \frac{[n]_q!}{[k]_q! [n-k]_q!}$
The following functions are exported for the calculation of q-deformed Wigner Symbols, which
serve a similar function as their
WignerSymbols.jl q-less counterparts:
q_wigner3j(j1, j2, j3, m1, m2, m3, q)q_clebschgorda(j1, j2, j3, m1, m2, m3, q)q_wigner6j(j1, j2, j3, j4, j5, j6, q)q_racahW(j1, j2, J, j3, J12, J23, q)
Finally, these can be utilized to construct q-deformed symmetric tensors, by using
SU2qIrrep{q} as a drop-in replacement for
TensorKit.jl's SU2Irrep:
using TensorKit, QWignerSymbols
q = 1.1
j = 1//2
irrep = SU2qIrrep{q}(j)
# Construct a rank-4 tensor with q-deformed SU(2) symmetry
t = TensorMap(randn, Float64, Vect[SU2qIrrep{q}](1//2 => 1)^2 ← Vect[SU2qIrrep{q}](1//2 => 1)^2)