Merge pull request #1 from phyjswang/U1andNoSymSpinLocalSpace

add U1 and no sym spin local space

example/Models/Heisenberg.jl

@@ -35,4 +35,51 @@ function SU₂Heisenberg(Latt::AbstractLattice; J::Number=1, J′::Number=0)
 
      return InteractionTree(Root)
 
-end
+end
+
+function U₁Heisenberg(Latt::AbstractLattice; J::Number=1, J′::Number=0)
+
+    # note J > 0 means AFM
+
+    Root = InteractionTreeNode(IdentityOperator(0), nothing)
+
+    # get the distance of NN and NNN pairs
+    lsd = map(1:length(Latt)) do i
+               metric(Latt, Latt[i])
+          end |> sort |> unique
+    i = 1
+    while i < length(lsd)
+         if lsd[i] ≈ lsd[i+1]
+              deleteat!(lsd, i + 1)
+         else
+              i += 1
+         end
+    end
+
+    let LocalSpace = U₁Spin
+
+         # NN interaction
+         for pairs in neighbor(Latt; d=lsd[1])
+              addIntr2!(Root, (LocalSpace.Sz, LocalSpace.Sz), pairs,
+                   J; name=(:Sz, :Sz))
+              addIntr2!(Root, LocalSpace.S₋₊, pairs,
+                   J/2; name=(:Sm, :Sp))
+              addIntr2!(Root, LocalSpace.S₊₋, pairs,
+                   J/2; name=(:Sp, :Sm))
+         end
+
+        # NNN interaction
+        for pairs in neighbor(Latt; d=lsd[2])
+            addIntr2!(Root, (LocalSpace.Sz, LocalSpace.Sz), pairs,
+                    J′; name=(:Sz, :Sz))
+            addIntr2!(Root, LocalSpace.S₋₊, pairs,
+                   J′/2; name=(:Sm, :Sp))
+            addIntr2!(Root, LocalSpace.S₊₋, pairs,
+                   J′/2; name=(:Sp, :Sm))
+        end
+
+    end
+
+    return InteractionTree(Root)
+
+end

src/FiniteMPS.jl

@@ -114,7 +114,7 @@ include("Observables/convert.jl")
 
 
 # predefined local spaces
-export SU₂Spin, SU2Spin, U₁SU₂Fermion, U1SU2Fermion, ℤ₂SU₂Fermion, Z2SU2Fermion, U₁SpinlessFermion, U1SpinlessFermion, U₁SU₂tJFermion, U1SU2tJFermion, U₁U₁Fermion, U1U1Fermion
+export SU₂Spin, SU2Spin, U₁Spin, U1Spin, NoSymSpinOneHalf, U₁SU₂Fermion, U1SU2Fermion, ℤ₂SU₂Fermion, Z2SU2Fermion, U₁SpinlessFermion, U1SpinlessFermion, U₁SU₂tJFermion, U1SU2tJFermion, U₁U₁Fermion, U1U1Fermion
 include("LocalSpace/Spin.jl")
 include("LocalSpace/Fermion.jl")
 include("LocalSpace/tJFermion.jl")

src/LocalSpace/Spin.jl

@@ -29,4 +29,100 @@ end
 """
      const SU2Spin = SU₂Spin
 """
-const SU2Spin = SU₂Spin
+const SU2Spin = SU₂Spin
+
+"""
+     module U₁Spin
+
+Prepare the local space of U₁ spin-1/2.
+
+# Fields
+     pspace::VectorSpace
+Local `d = 2` Hilbert space.
+
+    Sz::TensorMap
+Rank-`2` spin-z operator `Sz = (n↑ - n↓)/2`.
+
+    S₊₋::NTuple{2, TensorMap}
+    S₋₊::NTuple{2, TensorMap}
+Two rank-`3` operators of `S₊₋` and `S₋₊` interaction. Note Heisenberg `S⋅S = SzSz + (S₊₋ + S₋₊)/2`.
+"""
+module U₁Spin
+
+using TensorKit
+
+const pspace = Rep[U₁](-1 // 2 => 1, 1 // 2 => 1)
+
+const Sz = let
+     Sz = TensorMap(ones, pspace, pspace)
+     block(Sz, Irrep[U₁](1 // 2)) .= 1/2
+     block(Sz, Irrep[U₁](-1 // 2)) .= -1/2
+     Sz
+end
+
+# S+ S- interaction
+# convention: S⋅S = SzSz + (S₊₋ + S₋₊)/2
+const S₊₋ = let
+     aspace = Rep[U₁](1 => 1)
+     S₊ = TensorMap(ones, pspace, pspace ⊗ aspace)
+     S₋ = TensorMap(ones, aspace ⊗ pspace, pspace)
+     S₊, S₋
+end
+
+const S₋₊ = let
+     aspace = Rep[U₁](1 => 1)
+     iso = isometry(aspace, flip(aspace))
+     @tensor S₋[a; c d] := S₊₋[1]'[a, b, c] * iso'[d, b]
+     @tensor S₊[d a; c] := S₊₋[2]'[a, b, c] * iso[b, d]
+     S₋, S₊
+end
+
+end
+
+const U1Spin = U₁Spin
+
+"""
+     module NoSymSpinOneHalf
+
+Prepare the local space of U₁ spin-1/2. Basis convention is `{|↑⟩, |↓⟩}`.
+
+# Fields
+     pspace::VectorSpace
+Local `d = 2` Hilbert space.
+
+    Sz::TensorMap
+    Sx::TensorMap
+    Sy::TensorMap
+Rank-`2` spin-1/2 operators.
+
+    S₊::TensorMap
+Rank-`2` spin-plus operator `S₊ = Sx + iSy`.
+    S₋::TensorMap
+Rank-`2` spin-minus operator `S₋ = Sx - iSy`.
+"""
+module NoSymSpinOneHalf
+
+using TensorKit
+
+const pspace = ℂ^2
+
+const Sz = let
+     mat = Float64[1/2 0; 0 -1/2]
+     TensorMap(mat, pspace, pspace)
+end
+
+const S₊ = let
+    mat = Float64[0 1; 0 0]
+    TensorMap(mat, pspace, pspace)
+end
+
+const S₋ = let
+    mat = Float64[0 0; 1 0]
+    TensorMap(mat, pspace, pspace)
+end
+
+const Sx = (S₊ + S₋) / 2.
+
+const Sy = (S₊ - S₋) / (2. * 1im)
+
+end