Simplify spin one

Author: mtfishman

src/itensor/op.jl

@@ -70,7 +70,8 @@ function op(name::AbstractString, s::Index...; adjoint::Bool=false, kwargs...)
   ## end
 
   common_stypes = _sitetypes(commontags_s)
-  @ignore_derivatives push!(common_stypes, SiteType("Generic"))
+  # TODO: Delete this.
+  push!(common_stypes, SiteType("Generic"))
   opn = OpName(name)
   for st in common_stypes
     op_mat = AbstractArray(opn, st; kwargs...)

src/op.jl

@@ -182,9 +182,10 @@ alias(::OpName"X") = (OpName"σ⁺"() + OpName"σ⁻"()) / 2
 @op_alias "iX" "im" op = OpName"X"()
 @op_alias "√X" "√" op = OpName"X"()
 @op_alias "√NOT" "√" op = OpName"X"()
-alias(n::OpName"Sx") = OpName("X") / 2
+alias(n::OpName"Sx") = OpName"X"() / 2
 @op_alias "Sˣ" "Sx"
 @op_alias "Sₓ" "Sx"
+alias(::OpName"Sx2") = OpName"Sx"()^2
 
 alias(::OpName"Y") = -im * (OpName"σ⁺"() - OpName"σ⁻"()) / 2
 # TODO: No subsript `\_y` available
@@ -193,9 +194,7 @@ alias(::OpName"Y") = -im * (OpName"σ⁺"() - OpName"σ⁻"()) / 2
 @op_alias "σ2" "Y"
 @op_alias "σ²" "Y"
 @op_alias "σ₂" "Y"
-function alias(::OpName"iY")
-  return real(OpName"Y"()im)
-end
+alias(::OpName"iY") = (OpName"σ⁺"() - OpName"σ⁻"()) / 2
 @op_alias "iσy" "iY"
 # TODO: No subsript `\_y` available
 # in unicode.
@@ -207,6 +206,7 @@ alias(n::OpName"Sy") = OpName("Y") / 2
 @op_alias "Sʸ" "Sy"
 alias(n::OpName"iSy") = OpName("iY") / 2
 @op_alias "iSʸ" "iSy"
+alias(::OpName"Sy2") = -OpName"iSy"()^2
 
 function Base.AbstractArray(n::OpName"σᶻ", domain_size::Tuple{Int})
   d = only(domain_size)
@@ -221,7 +221,7 @@ end
 @op_alias "σ₃" "Z"
 @op_alias "σz" "Z"
 @op_alias "iZ" "im" op = OpName"Z"()
-alias(n::OpName"Sz") = OpName("Z") / 2
+alias(n::OpName"Sz") = OpName"Z"() / 2
 @op_alias "Sᶻ" "Sz"
 # TODO: Make sure it ends up real, using `S⁺` and `S⁻`,
 # define `Sx²`, `Sy²`, and `Sz²`, etc.
@@ -231,8 +231,9 @@ alias(n::OpName"Sz") = OpName("Z") / 2
 #   = (d - 1) * (d + 1) / 4 * I
 # ```
 # where `s = (d - 1) / 2`. See https://en.wikipedia.org/wiki/Spin_(physics)#Higher_spins.
-alias(n::OpName"S2") = (OpName("Sˣ")^2 + OpName("Sʸ")^2 + OpName("Sᶻ")^2)
+alias(n::OpName"S2") = OpName"Sx2"() + OpName"Sy2"() + OpName"Sz2"()
 @op_alias "S²" "S2"
+alias(::OpName"Sz2") = OpName"Sz"()^2
 
 using LinearAlgebra: eigen
 function Base.AbstractArray(n::OpName"H", domain_size::Tuple{Int})

src/sitetypes/spinone.jl

@@ -1,6 +1,8 @@
 # TODO: Need to define or replace.
 # using ITensorBase: complex!, QN
 
+Base.length(::SiteType"S=1") = 3
+
 alias(::SiteType"SpinOne") = SiteType"S=1"()
 
 """
@@ -54,97 +56,18 @@ state(::StateName"Y+", ::SiteType"S=1") = [-1 / 2, -im / sqrt(2), 1 / 2]
 state(::StateName"Y0", ::SiteType"S=1") = [1 / sqrt(2), 0, 1 / sqrt(2)]
 state(::StateName"Y-", ::SiteType"S=1") = [-1 / 2, im / sqrt(2), 1 / 2]
 
-op(::OpName"Id", ::SiteType"S=1") = [
-  1.0 0.0 0.0
-  0.0 1.0 0.0
-  0.0 0.0 1.0
-]
-
-op(::OpName"Sz", ::SiteType"S=1") = [
-  1.0 0.0 0.0
-  0.0 0.0 0.0
-  0.0 0.0 -1.0
-]
-
-op(on::OpName"Sᶻ", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"S+", ::SiteType"S=1") = [
-  0.0 √2 0.0
-  0.0 0.0 √2
-  0.0 0.0 0.0
-]
-
-op(on::OpName"S⁺", t::SiteType"S=1") = op(alias(on), t)
-op(on::OpName"Splus", t::SiteType"S=1") = op(alias(on), t)
-op(on::OpName"Sp", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"S-", ::SiteType"S=1") = [
-  0.0 0.0 0.0
-  √2 0.0 0.0
-  0.0 √2 0.0
-]
-
-op(on::OpName"S⁻", t::SiteType"S=1") = op(alias(on), t)
-op(on::OpName"Sminus", t::SiteType"S=1") = op(alias(on), t)
-op(on::OpName"Sm", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"Sx", ::SiteType"S=1") = [
-  0.0 1/√2 0.0
-  1/√2 0.0 1/√2
-  0.0 1/√2 0.0
-]
-
-op(on::OpName"Sˣ", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"iSy", ::SiteType"S=1") = [
-  0.0 1/√2 0.0
-  -1/√2 0.0 1/√2
-  0.0 -1/√2 0.0
-]
-
-op(on::OpName"iSʸ", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"Sy", ::SiteType"S=1") = [
-  0.0 -im/√2 0.0
-  im/√2 0.0 -im/√2
-  0.0 im/√2 0.0
-]
-
-op(on::OpName"Sʸ", t::SiteType"S=1") = op(alias(on), t)
-
-op(::OpName"Sz2", ::SiteType"S=1") = [
-  1.0 0.0 0.0
-  0.0 0.0 0.0
-  0.0 0.0 1.0
-]
-
-op(::OpName"Sx2", ::SiteType"S=1") = [
-  0.5 0.0 0.5
-  0.0 1.0 0.0
-  0.5 0.0 0.5
-]
-
-op(::OpName"Sy2", ::SiteType"S=1") = [
-  0.5 0.0 -0.5
-  0.0 1.0 0.0
-  -0.5 0.0 0.5
-]
-
-op(::OpName"S2", ::SiteType"S=1") = [
-  2.0 0.0 0.0
-  0.0 2.0 0.0
-  0.0 0.0 2.0
-]
-
-op(on::OpName"S²", t::SiteType"S=1") = op(alias(on), t)
-
+# TODO: Delete this.
 space(st::SiteType"SpinOne"; kwargs...) = space(alias(st); kwargs...)
 
+# TODO: Delete this.
 state(name::StateName, st::SiteType"SpinOne") = state(name, alias(st))
+# TODO: Delete this.
 val(name::ValName, st::SiteType"SpinOne") = val(name, alias(st))
 
+# TODO: Delete this.
 ## function op!(Op::ITensor, o::OpName, st::SiteType"SpinOne", s::Index)
 ##   return op!(Op, o, alias(st), s)
 ## end
 
+# TODO: Delete this.
 op(o::OpName, st::SiteType"SpinOne") = op(o, alias(st))