tensorkit v0.7.0 transition

Project.toml

@@ -1,7 +1,7 @@
 name = "MPSKit"
 uuid = "bb1c41ca-d63c-52ed-829e-0820dda26502"
-authors = ["Maarten Van Damme","Jutho Haegeman","Gertian Roose","Markus Hauru"]
-version = "0.2.0"
+authors = ["Maarten Van Damme", "Jutho Haegeman", "Gertian Roose", "Markus Hauru"]
+version = "0.3.0"
 
 [deps]
 KrylovKit = "0b1a1467-8014-51b9-945f-bf0ae24f4b77"
@@ -14,8 +14,8 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [compat]
 KrylovKit = "0.4 - 1"
+OptimKit = "0.1 - 1"
 Parameters = "0.12 - 1"
-julia = "1.4"
-TensorKit = "0.5 - 1"
+TensorKit = "0.7 - 1"
 TensorKitManifolds = "0.3 - 1"
-OptimKit = "0.1 - 1"
+julia = "1.4"

docs/src/man/intro.md

@@ -19,7 +19,7 @@ dat = rand(ComplexF64,10,10); TensorMap(dat,ℂ^10,ℂ^10);
 ```
 Similarly, the following creates a symmetric tensor
 ```julia
-TensorMap(rand,ComplexF64,ℂ[U₁](0=>1)*ℂ[U₁](1//2=>3),ℂ[U₁](1//2=>1,-1//2=>2))
+TensorMap(rand,ComplexF64,Rep[U₁](0=>1)*Rep[U₁](1//2=>3),Rep[U₁](1//2=>1,-1//2=>2))
 ```
 
 TensorKit defines a number of operations on TensorMap objects

docs/src/tut/haldane.md

@@ -17,8 +17,8 @@ ham = su2_xxx_ham(spin=1);
 The first step is always the same, we want to find the groundstate of our system.
 ```julia
 len = 10;
-physical_space = ℂ[SU₂](1=>1);
-virtual_space = ℂ[SU₂](0=>20,1=>20,2=>10,3=>10,4=>5);
+physical_space = Rep[SU₂](1=>1);
+virtual_space = Rep[SU₂](0=>20,1=>20,2=>10,3=>10,4=>5);
 
 initial_state = FiniteMPS(rand,ComplexF64,len,physical_space,virtual_space);
 (gs,pars,delta) = find_groundstate(initial_state,ham,Dmrg());
@@ -29,8 +29,8 @@ The typical way to find excited states is to minmize the energy while adding an
 In steven white's original DMRG paper it was remarked that the S=1 excitations correspond to edge states, and that one should define the haldane gap as the difference in energy between the S=2 and S=1 states. This can be done as follows.
 
 ```julia
-(En_1,st_1) = quasiparticle_excitation(ham,gs,pars,excitation_space = ℂ[SU₂](1=>1))
-(En_2,st_2) = quasiparticle_excitation(ham,gs,pars,excitation_space = ℂ[SU₂](2=>1))
+(En_1,st_1) = quasiparticle_excitation(ham,gs,pars,excitation_space = Rep[SU₂](1=>1))
+(En_2,st_2) = quasiparticle_excitation(ham,gs,pars,excitation_space = Rep[SU₂](2=>1))
 finite_haldane_gap = En_2[1]-En_1[1]
 ```
 
@@ -51,7 +51,7 @@ Extrapolating for different len gives an approximate haldane gap.
 A much nicer way of obtaining the haldane gap is by working directly in the thermodynamic limit. We must be careful in selecting the symmetry sectors, the only correct choice is to work with half-integer charges (this is an SPT phase).
 
 ```julia
-virtual_space = ℂ[SU₂](1//2=>20,3//2=>20,5//2=>10,7//2=>10,9//2=>5); # this is bond dimension 300!
+virtual_space = Rep[SU₂](1//2=>20,3//2=>20,5//2=>10,7//2=>10,9//2=>5); # this is bond dimension 300!
 initial_state = InfiniteMPS([physical_space],[virtual_space]);
 (gs,pars,delta) = find_groundstate(initial_state,ham,Vumps());
 ```
@@ -60,13 +60,13 @@ One difference with the finite size case is that we not only can - but also have
 
 ```julia
 kspace = 0:0.1:pi
-(Energies,_) = quasiparticle_excitation(ham,kspace,gs,pars,excitation_space=ℂ[SU₂](1=>1));
+(Energies,_) = quasiparticle_excitation(ham,kspace,gs,pars,excitation_space=Rep[SU₂](1=>1));
 ```
 ![](haldane_dispersion.png)
 
 The minimima sits at k = pi, with corresponding value
 
 ```julia
-(En,_) = quasiparticle_excitation(ham,Float64(pi),gs,pars,excitation_space=ℂ[SU₂](1=>1));
+(En,_) = quasiparticle_excitation(ham,Float64(pi),gs,pars,excitation_space=Rep[SU₂](1=>1));
 @assert En[1]  ≈ 0.41047925 atol=1e-4
 ```

docs/src/tut/xxz_groundstate.md

@@ -87,15 +87,15 @@ The xxz hamiltonian is su(2) symmetric and we can exploit this to greatly speed
 It is cumbersome to construct symmetric hamiltonians, but luckily su(2) symmetric xxz is already implemented:
 ```julia
 ham = repeat(su2_xxx_ham(spin=1//2),2);
-@assert ham.pspaces[1] == ℂ[SU₂](1//2 => 1)
+@assert ham.pspaces[1] == Rep[SU₂](1//2 => 1)
 ```
 Our initial state should also be su(2) symmetric. It now becomes apparant why we have to use a 2 site periodic state. The physical space carries a half-integer charge and the first tensor maps the first virtual space ⊗ the physical space to the second virtual space. Half integer virtual charges will therefore map only to integer charges, and vice versa. The staggering happens on the virtual level!
 
 An alternative constructor for the initial state is
 ```julia
-D1 = ℂ[SU₂](1//2 => 10,3//2=>5,5//2=>2);
-D2 = ℂ[SU₂](0=>15,1=>10,2=>5);
-state = InfiniteMPS([ℂ[SU₂](1//2 => 1),ℂ[SU₂](1//2 => 1)],[D1,D2])
+D1 = Rep[SU₂](1//2 => 10,3//2=>5,5//2=>2);
+D2 = Rep[SU₂](0=>15,1=>10,2=>5);
+state = InfiniteMPS([Rep[SU₂](1//2 => 1),Rep[SU₂](1//2 => 1)],[D1,D2])
 ```
 
 Even though the bond dimension is higher then in the non symmetric example:

src/algorithms/propagator/corvector.jl

@@ -74,10 +74,10 @@ function squaredenvs(state::Union{MPSComoving,FiniteMPS},ham::MPOHamiltonian,par
     for i in 1:ham.odim
         for j in 1:ham.odim
             @tensor temp[-1 -2 -3;-4]:=leftenv(pars,1,state)[j][1,-3,-4]*conj(leftenv(pars,1,state)[i][1,-2,-1])
-            copyto!(nleft[indmap(i,j)].data,temp.data)
+            copy!(nleft[indmap(i,j)].data,temp.data)
 
             @tensor temp[-1 -2 -3;-4]:=rightenv(pars,length(state),state)[j][-1,-2,1]*conj(rightenv(pars,length(state),state)[i][-4,-3,1])
-            copyto!(nright[indmap(i,j)].data,temp.data)
+            copy!(nright[indmap(i,j)].data,temp.data)
         end
     end
 

src/models/grossneveu.jl

@@ -1,35 +1,35 @@
 function su2u1_grossneveu(;g2SPT=0,g2AFM=0)
-    ph       = ℂ[SU₂×U₁]( (1//2,0)=>1, (0,-1)=>1, (0,1)=>1 )
-    bigonleg = ℂ[SU₂×U₁]( (0,0)=>1, (1//2,-1)=>1, (1//2,1)=>1 )
+    ph       = Rep[SU₂×U₁]( (1//2,0)=>1, (0,-1)=>1, (0,1)=>1 )
+    bigonleg = Rep[SU₂×U₁]( (0,0)=>1, (1//2,-1)=>1, (1//2,1)=>1 )
     unit     = oneunit(ph)
 
     LK = TensorMap(ones, ComplexF64, unit*ph, bigonleg*ph)
-    blocks(LK)[SU₂(0)×U₁(-1)]    =  [im*2/sqrt(2) 1]
-    blocks(LK)[SU₂(1//2)×U₁(0)] =  [1. im -im]
-    blocks(LK)[SU₂(0)×U₁(1)]    =  [im*2/sqrt(2) 1]
+    blocks(LK)[Irrep[SU₂](0)⊠Irrep[U₁](-1)]    =  [im*2/sqrt(2) 1]
+    blocks(LK)[Irrep[SU₂](1//2)⊠Irrep[U₁](0)] =  [1. im -im]
+    blocks(LK)[Irrep[SU₂](0)⊠Irrep[U₁](1)]    =  [im*2/sqrt(2) 1]
 
     RK = TensorMap(ones, ComplexF64, bigonleg*ph, unit*ph)
-    blocks(RK)[SU₂(0)×U₁(-1)][:]    =  [2/sqrt(2) 1][:]
-    blocks(RK)[SU₂(1//2)×U₁(0)][:] =  [1 -1 1][:]
-    blocks(RK)[SU₂(0)×U₁(1)][:]    =  [2/sqrt(2) 1][:]
+    blocks(RK)[Irrep[SU₂](0)⊠Irrep[U₁](-1)][:]    =  [2/sqrt(2) 1][:]
+    blocks(RK)[Irrep[SU₂](1//2)⊠Irrep[U₁](0)][:] =  [1 -1 1][:]
+    blocks(RK)[Irrep[SU₂](0)⊠Irrep[U₁](1)][:]    =  [2/sqrt(2) 1][:]
 
     Cplus = TensorMap(ones, ComplexF64, bigonleg*ph, bigonleg*ph)
-    blocks(Cplus)[SU₂(1//2)×U₁(0)]  = [0 im*0.5 -im*0.5; -0.5 0 0; 0.5 0 0]
-    blocks(Cplus)[SU₂(0)×U₁(-1)]     = [0 0.5*sqrt(2); im*0.5*sqrt(2) 0]
-    blocks(Cplus)[SU₂(1)×U₁(-1)]     = zeros(1,1)
-    blocks(Cplus)[SU₂(0)×U₁(1)]     = [0 0.5*sqrt(2); im*0.5*sqrt(2) 0]
-    blocks(Cplus)[SU₂(1)×U₁(1)]     = zeros(1,1)
-    blocks(Cplus)[SU₂(1//2)×U₁(-2)] = zeros(1,1)
-    blocks(Cplus)[SU₂(1//2)×U₁(2)]  = zeros(1,1)
+    blocks(Cplus)[Irrep[SU₂](1//2)⊠Irrep[U₁](0)]  = [0 im*0.5 -im*0.5; -0.5 0 0; 0.5 0 0]
+    blocks(Cplus)[Irrep[SU₂](0)⊠Irrep[U₁](-1)]     = [0 0.5*sqrt(2); im*0.5*sqrt(2) 0]
+    blocks(Cplus)[Irrep[SU₂](1)⊠Irrep[U₁](-1)]     = zeros(1,1)
+    blocks(Cplus)[Irrep[SU₂](0)⊠Irrep[U₁](1)]     = [0 0.5*sqrt(2); im*0.5*sqrt(2) 0]
+    blocks(Cplus)[Irrep[SU₂](1)⊠Irrep[U₁](1)]     = zeros(1,1)
+    blocks(Cplus)[Irrep[SU₂](1//2)⊠Irrep[U₁](-2)] = zeros(1,1)
+    blocks(Cplus)[Irrep[SU₂](1//2)⊠Irrep[U₁](2)]  = zeros(1,1)
 
     Cmin = TensorMap(ones, ComplexF64, bigonleg*ph, bigonleg*ph)
-    blocks(Cmin)[SU₂(1//2)×U₁(0)]  = conj([0 im*0.5 -im*0.5; -0.5 0 0; 0.5 0 0])
-    blocks(Cmin)[SU₂(0)×U₁(-1)]     = conj([0 0.5*sqrt(2); im*0.5*sqrt(2) 0])
-    blocks(Cmin)[SU₂(1)×U₁(-1)]     = zeros(1,1)
-    blocks(Cmin)[SU₂(0)×U₁(1)]     = conj([0 0.5*sqrt(2); im*0.5*sqrt(2) 0])
-    blocks(Cmin)[SU₂(1)×U₁(1)]     = zeros(1,1)
-    blocks(Cmin)[SU₂(1//2)×U₁(-2)] = zeros(1,1)
-    blocks(Cmin)[SU₂(1//2)×U₁(2)]  = zeros(1,1)
+    blocks(Cmin)[Irrep[SU₂](1//2)⊠Irrep[U₁](0)]  = conj([0 im*0.5 -im*0.5; -0.5 0 0; 0.5 0 0])
+    blocks(Cmin)[Irrep[SU₂](0)⊠Irrep[U₁](-1)]     = conj([0 0.5*sqrt(2); im*0.5*sqrt(2) 0])
+    blocks(Cmin)[Irrep[SU₂](1)⊠Irrep[U₁](-1)]     = zeros(1,1)
+    blocks(Cmin)[Irrep[SU₂](0)⊠Irrep[U₁](1)]     = conj([0 0.5*sqrt(2); im*0.5*sqrt(2) 0])
+    blocks(Cmin)[Irrep[SU₂](1)⊠Irrep[U₁](1)]     = zeros(1,1)
+    blocks(Cmin)[Irrep[SU₂](1//2)⊠Irrep[U₁](-2)] = zeros(1,1)
+    blocks(Cmin)[Irrep[SU₂](1//2)⊠Irrep[U₁](2)]  = zeros(1,1)
 
     f1 = isomorphism(fuse(unit, unit), unit*unit)
     f2 = isomorphism(bigonleg*bigonleg, fuse(bigonleg, bigonleg))
@@ -42,17 +42,9 @@ function su2u1_grossneveu(;g2SPT=0,g2AFM=0)
 
     #and now with the extra O(4) breaking part ie the O operator
     O_op = TensorMap(zeros, ComplexF64, unit*ph, unit*ph)
-    blocks(O_op)[SU₂(1//2)×U₁(0)] = -zeros(1,1)
-    blocks(O_op)[SU₂(0)×U₁(-1)]    =  -1*ones(1,1)
-    blocks(O_op)[SU₂(0)×U₁(1)]    =  1*ones(1,1)
-
-
-    #=
-    BlockHamiltonian([ SimpleLocalMPO([LK , Cplus, RK]) ,
-            SimpleLocalMPO([-0.25*g2SPT^2*Ldiffsq, Cdiffsq, Rdiffsq]) ,
-            SimpleLocalMPO([-0.5*g2AFM^2*O_op^2]),
-            SimpleLocalMPO([+0.5*g2AFM^2*O_op, O_op])   ])
-    =#
+    blocks(O_op)[Irrep[SU₂](1//2)⊠Irrep[U₁](0)] = -zeros(1,1)
+    blocks(O_op)[Irrep[SU₂](0)⊠Irrep[U₁](-1)]    =  -1*ones(1,1)
+    blocks(O_op)[Irrep[SU₂](0)⊠Irrep[U₁](1)]    =  1*ones(1,1)
 
     MPOHamiltonian([LK, Cplus, RK]) +
     MPOHamiltonian([-0.25*g2SPT^2*Ldiffsq, Cdiffsq, Rdiffsq]) +

src/models/xxz.jl

@@ -13,10 +13,10 @@ end
 
 function su2_xxx_ham(;spin = 1//2)
     #only checked for spin = 1 and spin = 2...
-    ph = ℂ[SU₂](spin=>1)
+    ph = Rep[SU₂](spin=>1)
 
-    Sl1 = TensorMap(ones, Defaults.eltype, ℂ[SU₂](0=>1)*ph , ℂ[SU₂](1=>1)*ph)*sqrt(spin^2+spin)
-    Sr1 = TensorMap(ones, Defaults.eltype, ℂ[SU₂](1=>1)*ph , ℂ[SU₂](0=>1)*ph)*sqrt(spin^2+spin)
+    Sl1 = TensorMap(ones, Defaults.eltype, Rep[SU₂](0=>1)*ph , Rep[SU₂](1=>1)*ph)*sqrt(spin^2+spin)
+    Sr1 = TensorMap(ones, Defaults.eltype, Rep[SU₂](1=>1)*ph , Rep[SU₂](0=>1)*ph)*sqrt(spin^2+spin)
 
     return MPOHamiltonian([Sl1,Sr1]);
 end
@@ -25,14 +25,14 @@ function u1_xxz_ham(;spin = 1,delta = 1,zfield = 0.0)
     (sxd,syd,szd,idd) = spinmatrices(spin);
     @tensor ham[-1 -2;-3 -4]:=sxd[-1,-3]*sxd[-2,-4]+syd[-1,-3]*syd[-2,-4]+(delta*szd)[-1,-3]*szd[-2,-4]+zfield*0.5*szd[-1,-3]*idd[-2,-4]+zfield*0.5*idd[-1,-3]*szd[-2,-4]
 
-    indu1map = [U₁(v) for v in -spin:1:spin];
+    indu1map = [Irrep[U₁](v) for v in -spin:1:spin];
     pspace = U1Space((v=>1 for v in indu1map));
 
     symham = TensorMap(zeros,eltype(ham),pspace*pspace,pspace*pspace)
 
     for (i,j,k,l) in Iterators.product(1:size(ham,1),1:size(ham,1),1:size(ham,1),1:size(ham,1))
         if ham[i,j,k,l]!=0
-            copyto!(symham[(indu1map[i],indu1map[j],indu1map[k],indu1map[l])],ham[i,j,k,l])
+            copy!(symham[(indu1map[i],indu1map[j],indu1map[end-k+1],indu1map[end-l+1])],ham[i:i,j:j,k:k,l:l])
         end
     end
 

src/states/comoving.jl

@@ -66,11 +66,11 @@ function MPSComoving(f, elt, physspaces::Vector{<:Union{S,CompositeSpace{S}}}, m
     virtspaces = Vector{S}(undef, N+1)
     virtspaces[1] = left
     for k = 2:N
-        virtspaces[k] = infinum(fuse(virtspaces[k-1], fuse(physspaces[k])), maxvirtspace)
+        virtspaces[k] = infimum(fuse(virtspaces[k-1], fuse(physspaces[k])), maxvirtspace)
     end
     virtspaces[N+1] = right
     for k = N:-1:2
-        virtspaces[k] = infinum(virtspaces[k], fuse(virtspaces[k+1], flip(fuse(physspaces[k]))))
+        virtspaces[k] = infimum(virtspaces[k], fuse(virtspaces[k+1], flip(fuse(physspaces[k]))))
     end
     return MPSComoving(f, elt,physspaces, virtspaces,leftgs,rightgs)
 end

src/states/finitemps.jl

@@ -76,11 +76,11 @@ function FiniteMPS(f, elt, physspaces::Vector{<:Union{S,CompositeSpace{S}}}, max
     virtspaces = Vector{S}(undef, N+1)
     virtspaces[1] = left
     for k = 2:N
-        virtspaces[k] = infinum(fuse(virtspaces[k-1], fuse(physspaces[k])), maxvirtspace)
+        virtspaces[k] = infimum(fuse(virtspaces[k-1], fuse(physspaces[k])), maxvirtspace)
     end
     virtspaces[N+1] = right
     for k = N:-1:2
-        virtspaces[k] = infinum(virtspaces[k], fuse(virtspaces[k+1], flip(fuse(physspaces[k]))))
+        virtspaces[k] = infimum(virtspaces[k], fuse(virtspaces[k+1], flip(fuse(physspaces[k]))))
     end
     return FiniteMPS(f, elt,physspaces, virtspaces)
 end

src/states/quasiparticle_state.jl

@@ -4,7 +4,7 @@ I think it makes sense to see these things as an actual state instead of return
 This will allow us to plot energy density (finite qp) and measure observeables.
 =#
 
-struct FiniteQP{S<:FiniteMPS,T1,T2}
+struct FiniteQP{S<:Union{MPSComoving,FiniteMPS},T1,T2}
     # !(left_gs === right_gs) => domain wall excitation
     left_gs::S
     right_gs::S
@@ -14,7 +14,7 @@ struct FiniteQP{S<:FiniteMPS,T1,T2}
 
 end
 
-function rand_quasiparticle(left_gs::FiniteMPS,right_gs=left_gs;excitation_space=oneunit(virtualspace(left_gs,1)))
+function rand_quasiparticle(left_gs::Union{MPSComoving,FiniteMPS},right_gs=left_gs;excitation_space=oneunit(virtualspace(left_gs,1)))
     #find the left null spaces for the TNS
     VLs = [adjoint(rightnull(adjoint(v))) for v in left_gs.AL]
     Xs = [TensorMap(rand,eltype(left_gs.AL[1]),space(VLs[loc],3)',excitation_space'*space(right_gs.AR[ loc],3)') for loc in 1:length(left_gs)]
@@ -44,10 +44,11 @@ end
 const QP = Union{InfiniteQP,FiniteQP};
 
 utilleg(v::QP) = space(v.Xs[1],2)
-Base.copy(a::QP) = copyto!(similar(a),a)
-function Base.copyto!(a::QP,b::QP)
+Base.copy(a::QP) = copy!(similar(a),a)
+Base.copyto!(a::QP,b::QP) = copy!(a,b);
+function Base.copy!(a::QP,b::QP)
     for (i,j) in zip(a.Xs,b.Xs)
-        copyto!(i,j)
+        copy!(i,j)
     end
     a
 end

test/runtests.jl

@@ -5,7 +5,7 @@ println("|     States                       |")
 println("------------------------------------")
 @testset "FiniteMPS ($D,$d,$elt)" for (D,d,elt) in [
         (ComplexSpace(10),ComplexSpace(2),ComplexF64),
-        (ℂ[SU₂](1=>1,0=>3),ℂ[SU₂](0=>1)*ℂ[SU₂](0=>1),ComplexF32)
+        (Rep[SU₂](1=>1,0=>3),Rep[SU₂](0=>1)*Rep[SU₂](0=>1),ComplexF32)
         ]
 
     ts = FiniteMPS(rand,elt,rand(3:20),d,D);
@@ -28,7 +28,7 @@ end
 
 @testset "InfiniteMPS ($D,$d,$elt)" for (D,d,elt) in [
         (ComplexSpace(10),ComplexSpace(2),ComplexF64),
-        (ℂ[U₁](1=>3),ℂ[U₁](0=>1),ComplexF64)
+        (Rep[U₁](1=>3),Rep[U₁](0=>1),ComplexF64)
         ]
     tol = Float64(eps(real(elt))*100);
 
@@ -52,7 +52,7 @@ end
 
 @testset "MPSMultiline ($D,$d,$elt)" for (D,d,elt) in [
         (ComplexSpace(10),ComplexSpace(2),ComplexF64),
-        (ℂ[U₁](1=>3),ℂ[U₁](0=>1),ComplexF32)
+        (Rep[U₁](1=>3),Rep[U₁](0=>1),ComplexF32)
         ]
 
     tol = Float64(eps(real(elt))*100);
@@ -123,7 +123,7 @@ end
 @testset "Quasiparticle state" begin
     @testset "Finite" for (th,D,d) in [
         (nonsym_ising_ham(),ComplexSpace(10),ComplexSpace(2)),
-        (su2_xxx_ham(spin=1),ℂ[SU₂](1=>1,0=>3),ℂ[SU₂](1=>1))
+        (su2_xxx_ham(spin=1),Rep[SU₂](1=>1,0=>3),Rep[SU₂](1=>1))
         ]
 
 
@@ -149,7 +149,7 @@ end
 
     @testset "Infinite" for (th,D,d) in [
         (nonsym_ising_ham(),ComplexSpace(10),ComplexSpace(2)),
-        (su2_xxx_ham(spin=1),ℂ[SU₂](1=>1,0=>3),ℂ[SU₂](1=>1))
+        (su2_xxx_ham(spin=1),Rep[SU₂](1=>1,0=>3),Rep[SU₂](1=>1))
         ]
 
         period = rand(1:4);
@@ -170,8 +170,8 @@ println("|     Operators                    |")
 println("------------------------------------")
 @testset "mpoham $(i)" for (i,(th,Dspaces)) in enumerate([
         (nonsym_ising_ham(),[ℂ^1]),
-        (u1_xxz_ham(),[ℂ[U₁](1//2=>1)]),
-        (repeat(su2_xxx_ham(),2),[ℂ[SU₂](0=>1),ℂ[SU₂](1//2=>1)])
+        (u1_xxz_ham(),[Rep[U₁](1//2=>1)]),
+        (repeat(su2_xxx_ham(),2),[Rep[SU₂](0=>1),Rep[SU₂](1//2=>1)])
         ])
 
     ts = InfiniteMPS(th.pspaces,Dspaces); # generate a product state