Dealing with Fermions

function bosonize(oppair::Vector{Pair{String, Int}},
                  sites::Vector{Index})

Given a string of operator names with positions in the form of Vector{Pair{String, Int}} "bosonizes" the operator string by putting the Jordan-Wigner string "F" at appropriate places.

Arguments

• oppair::Vector{Pair{String, Int}}: Input string of operator names with positions.
• sites::Vector{Index}: The entire site Indexs as per ITensors' convention.

Return values

• ::Int: Even (+1) or odd (-1) permutation.
• ::Vector{Pair{String, Int}}: modified string of operator names and positions.