[ITensors] Define Sy for tJ site type (#1642)

Author: andrewkhardy

src/lib/SiteTypes/src/sitetypes/tj.jl

@@ -183,7 +183,13 @@ function op!(Op::ITensor, ::OpName"Sx", ::SiteType"tJ", s::Index)
   Op[s' => 2, s => 3] = 0.5
   return Op[s' => 3, s => 2] = 0.5
 end
-
+function op!(Op::ITensor, ::OpName"Sy", ::SiteType"tJ", s::Index)
+  Op[s' => 2, s => 3] = -0.5im
+  return Op[s' => 3, s => 2] = 0.5im
+end
+function op!(Op::ITensor, ::OpName"Sʸ", st::SiteType"tJ", s::Index)
+  return op!(Op, OpName("Sy"), st, s)
+end
 function op!(Op::ITensor, ::OpName"Sˣ", st::SiteType"tJ", s::Index)
   return op!(Op, OpName("Sx"), st, s)
 end

test/base/test_phys_site_types.jl

@@ -742,6 +742,10 @@ using ITensors.SiteTypes: has_fermion_string, op, siteind, siteinds, state
     @test Sx ≈ [0.0 0.0 0; 0 0 0.5; 0 0.5 0]
     Sx = Array(op(s, "Sˣ"), s', s)
     @test Sx ≈ [0.0 0.0 0; 0 0 0.5; 0 0.5 0]
+    Sy = Array(op(s, "Sy"), s', s)
+    @test Sy ≈ [0.0 0.0 0; 0 0 -0.5im; 0 0.5im 0]
+    Sy = Array(op(s, "Sʸ"), s', s)
+    @test Sy ≈ [0.0 0.0 0; 0 0 -0.5im; 0 0.5im 0]
     Sp = Array(op(s, "Splus"), s', s)
     @test Sp ≈ [0.0 0.0 0; 0 0 1.0; 0 0 0]
     Sp = Array(op(s, "Sp"), s', s)