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add spin irreducible operators with U(1) and SU(2) #24

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add spin irreducible operators with U(1) and SU(2) #24

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bbd2020
add spin irreducible operators
ZongYongyue Aug 5, 2024
adec3f7
add S_e,S_e_square,S_e_exchange
ZongYongyue Aug 5, 2024
a6ff2bd
change spin operator to MPSKitModels style
ZongYongyue Aug 6, 2024
9077a7b
export spin operators
ZongYongyue Aug 6, 2024
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29 changes: 29 additions & 0 deletions src/operators/fermionoperators.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -229,3 +229,32 @@ function e_number_updown(elt::Type{<:Number}, ::Type{U1Irrep}, ::Type{SU2Irrep})
end

const nꜛnꜜ = e_number_updown

function S_e(elt::Type{<:Number}, ::Type{U1Irrep}, ::Type{SU2Irrep})
pspace = Vect[fℤ₂ ⊠ U1Irrep ⊠ SU2Irrep]((0, 0, 0) => 1, (1, 1, 1 // 2) => 1,
(0, 2, 0) => 1)
vspace = Vect[fℤ₂ ⊠ U1Irrep ⊠ SU2Irrep]((0, 0, 1) => 1)
S = TensorMap(zeros, elt, pspace ← pspace ⊗ vspace)
blocks(S)[fℤ₂(1) ⊠ U1Irrep(1) ⊠ SU2Irrep(1 // 2)] .= sqrt(3)/2
return S
end

const Sₑ = S_e

function S_e_square(elt::Type{<:Number}, ::Type{U1Irrep}, ::Type{SU2Irrep})
pspace = Vect[fℤ₂ ⊠ U1Irrep ⊠ SU2Irrep]((0, 0, 0) => 1, (1, 1, 1 // 2) => 1,
(0, 2, 0) => 1)
S2 = TensorMap(zeros, elt, pspace ← pspace)
blocks(S2)[fℤ₂(1) ⊠ U1Irrep(1) ⊠ SU2Irrep(1 // 2)] .= 3/4
return S2
end

const Sₑ² = S_e_square

function S_e_exchange(elt::Type{<:Number}, ::Type{U1Irrep}, ::Type{SU2Irrep})
S = S_e(elt, U1Irrep, SU2Irrep)
@planar SS[-1 -2; -3 -4] := S[-1;-3 1]*permute(S',((2,1),(3,)))[1 -2; -4]
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I'm a bit confused by the explicit call to permute here. Is this not the same as (S')[-2 1; -4] ?
Alternatively, I think if you want you can make this the same system as for the other "one-sided" operators:

The S_e gets a keyword argument side=:L or side=:R, and then you can make use of the contract_twosite function to combine them?

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Ok, no problem

return SS
end

const S_e_exchange = SₑSₑ