Merge pull request #60 from iitis/lp/identities

Introduce the concpept of identity MPS and MPO

src/SpinGlassPEPS.jl

@@ -16,6 +16,7 @@ module SpinGlassPEPS
     include("utils.jl")
     include("compressions.jl")
     include("contractions.jl")
+    include("identities.jl")
     include("lattice.jl")
     #include("graphs/chimera.jl")
     #include("graphs/lattice.jl")

src/contractions.jl

@@ -105,9 +105,10 @@ function LinearAlgebra.dot(ϕ::AbstractMPS, O::Union{Vector, NTuple}, ψ::Abstra
 end
 
 
-function LinearAlgebra.dot(O::AbstractMPO, ψ::T) where {T <: AbstractMPS}
+function LinearAlgebra.dot(O::AbstractMPO, ψ::AbstractMPS)
     L = length(ψ)
     S = promote_type(eltype(ψ), eltype(O))
+    T = typeof(ψ)
     ϕ = T.name.wrapper(S, L)
 
     for i ∈ 1:L

src/identities.jl

@@ -0,0 +1,26 @@
+export IdentityMPO, IdentityMPS
+struct IdentityMPS{T <: Number} <: AbstractMPS{T} end
+struct IdentityMPO{T <: Number} <: AbstractMPO{T} end
+
+@inline Base.getindex(::IdentityMPS{T}, ::Int) where {T} = ones(T, 1, 1, 1)
+@inline Base.getindex(::IdentityMPO{T}, ::Int) where {T} = ones(T, 1, 1, 1, 1)
+
+MPS(::UniformScaling{T}) where {T} = IdentityMPS{T}()
+MPO(::UniformScaling{T}) where {T} = IdentityMPO{T}()
+
+LinearAlgebra.dot(O::AbstractMPO, ::IdentityMPO) = O
+LinearAlgebra.dot(::IdentityMPO, O::AbstractMPO) = O
+
+function LinearAlgebra.dot(O::AbstractMPO, ::IdentityMPS)
+    L = length(O)
+    T = eltype(O)
+    ψ = MPS(T, L)
+    for i ∈ eachindex(ψ)
+        B = O[i]
+        @reduce A[x, σ, y] |= sum(η) B[x, σ, y, η]
+        ψ[i] = A
+    end
+    ψ
+end
+
+LinearAlgebra.dot(::IdentityMPO, ψ::AbstractMPS) = ψ

test/identities.jl

@@ -0,0 +1,21 @@
+@testset "multiplication of identities" begin
+    ψ = randn(MPS{Float64}, 4, 3, 2)
+    O = randn(MPO{Float64}, 4, 3, 2)
+
+    IMPS = MPS(I)
+    IMPO = MPO(I)
+
+    @test IMPO * ψ == ψ
+    @test IMPO * O == O
+
+    ϕ = O * IMPS
+
+    @test typeof(ϕ) == MPS{Float64}
+    @test length(ϕ) == length(O)
+
+    for i ∈ eachindex(O)
+        @test ϕ[i] == dropdims(sum(O[i], dims=4), dims=4)
+    end
+
+    @test IMPO === MPO(I)
+end

test/runtests.jl

@@ -28,6 +28,7 @@ push!(my_tests,
     "utils.jl",
     "contractions.jl",
     "compressions.jl",
+    "identities.jl",
     "ising.jl",
     "indexing.jl",
     "searchMPS.jl",