+1 vote
asked by (640 points)
reopened by

I try to use Trotter Gates. When I use the following snippet

for(int b = 1; b <= N-1; ++b)
auto hterm = sites.op("Sx",b)*sites.op("Sx",b+1);
auto g = Gate(sites,b,b+1,Gate::tReal,tstep/2.,hterm);

the program calculate nothing. However, when i use "Sz" rather than "Sx" the program works well. I noticed in http://itensor.org/docs.cgi?vers=cppv2&page=classes/spinhalf that
"Sx" must be converted to an ITensor prior to usage. Could you please say how this can be done?

1 Answer

+1 vote
answered by (70.1k points)
selected by
Best answer

Yes this is an unfortunate issue with version 2 of ITensor. The soon to be released version 3 will fix this issue.

By convert to ITensor, what is meant is this:

ITensor Sxb = sites.op(“Sx”,b);

And similar for the other operator. Then you can multiply these ITensors together.

commented by (270 points)
Is there a Julia version for this? Met same problem...
commented by (70.1k points)
Hi, could you please clarify your question. When you say a Julia version for "this" do you mean obtaining operators from the `op` function? Or are you referring this specific issue about the Sx operator in ITensor version 2 and whether the Julia version has a similar issue? Or something else?

commented by (270 points)
Sorry for not describing this clearly. My problem is also about Sx and Sy. I have a spin Hamiltonian in the form: \sum_ j { A(S+_j S-_j+1  + S-_j S+_j+1) + B(Sz_j Sz_j+1 - C),  you know just a regular 1D spin 1/2 model. Then I calculated the ground state of it, and just want to print <Sx>, <Sy>, <Sz> at each site with the ground state.  So after I get the ground state, I tried the following. But it only works when I only have Sz, and gave error message when including Sx and Sy. ( I attach the error message at the end, sorry it's a bit long...) I'm not sure if it's due to same issue, so just want to try this command "ITensor Sxb = sites.op(“Sx”,b);" in julia version...

      sx1 = fill(0.0, N)
      sy1 = fill(0.0, N)
      sz1 = fill(0.0, N)
      for j in 1:N
        orthogonalize!(psi1, j)
        psidag1_j = dag(prime(psi1[j], "Site"))
        sx1[j] = scalar(psidag1_j * op(sites,"Sx",j) * psi1[j])
        sy1[j] = scalar(psidag1_j * op(sites,"Sy",j) * psi1[j])
        sz1[j] = scalar(psidag1_j * op(sites,"Sz",j) * psi1[j])

       for j in 1:N

      for j in 1:N
       for j in 1:N

ERROR: LoadError: In `setindex!`, the element (1, 2) of ITensor:
Dim 1: (dim=2|id=808|"S=1/2,Site,n=1")' <Out>
 1: QN("Sz",1) => 1
 2: QN("Sz",-1) => 1
Dim 2: (dim=2|id=808|"S=1/2,Site,n=1") <In>
 1: QN("Sz",1) => 1
 2: QN("Sz",-1) => 1
NDTensors.BlockSparse{Float64, Vector{Float64}, 2}
Block(2, 1)
 [2:2, 1:1]
 you are trying to set is in a block with flux QN("Sz",2), which is different from the flux QN("Sz",-2) of the other blocks of the ITensor. You may be trying to create an ITensor that does not have a well defined quantum number flux.
  [1] error(s::String)
    @ Base ./error.jl:33
  [2] _setindex!!(::ITensors.HasQNs, ::NDTensors.BlockSparseTensor{Float64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{Float64, Vector{Float64}, 2}}, ::Float64, ::Int64, ::Int64)
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/qn/qnitensor.jl:7
  [3] _setindex!!
    @ ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:928 [inlined]
  [4] setindex!
    @ ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:970 [inlined]
  [5] setindex!(T::ITensor, x::Float64, I::CartesianIndex{2})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:974
  [6] ITensor(::NDTensors.AllowAlias, ::Type{Float64}, A::Matrix{Float64}, inds::Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}; tol::Int64)
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/qn/qnitensor.jl:295
  [7] ITensor(::NDTensors.AllowAlias, ::Type{Float64}, A::Matrix{Float64}, inds::Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/qn/qnitensor.jl:284
  [8] ITensor(::NDTensors.AllowAlias, ::Matrix{Float64}, ::Index{Vector{Pair{QN, Int64}}}, ::Vararg{Index{Vector{Pair{QN, Int64}}}}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:497
  [9] ITensor(::NDTensors.AllowAlias, ::Matrix{Float64}, ::Index{Vector{Pair{QN, Int64}}}, ::Vararg{Index{Vector{Pair{QN, Int64}}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:497
 [10] itensor(::Matrix{Float64}, ::Vararg{Any}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:123
 [11] itensor(::Matrix{Float64}, ::Index{Vector{Pair{QN, Int64}}}, ::Vararg{Index{Vector{Pair{QN, Int64}}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/itensor.jl:123
 [12] op(name::String, s::Index{Vector{Pair{QN, Int64}}}; kwargs::Base.Pairs{Symbol, Union{}, Tuple{}, NamedTuple{(), Tuple{}}})
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:260
 [13] op
    @ ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:221 [inlined]
 [14] #op#947
    @ ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:355 [inlined]
 [15] op
    @ ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:355 [inlined]
 [16] #op#952
    @ ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:369 [inlined]
 [17] op(s::Vector{Index{Vector{Pair{QN, Int64}}}}, opname::String, ns::Int64)
    @ ITensors ~/.julia/packages/ITensors/5sSxp/src/physics/sitetype.jl:369
 [18] top-level scope
    @ ~/dmrg/spin.jl:113
commented by (70.1k points)
I see, yes so the way our QN conserving ITensor system works is that you are only allowed to form ITensor which change the total QN of a state by a well-defined amount. The Sx operator doesn't have this property so it can't be made when you are conserving total Sz quantum numbers (setting conserve_qns=true when making your site indices).

On a related note, though, the expectation value of <Sx> is always guaranteed to be zero for a state with a well-defined total Sz quantum number. So you can know analytically that <Sx> will be zero.

But of course there are cases where you want to measure something like <Sx_i Sx_j> which can be non-zero even if total Sz is conserved. For those cases, you should use the fact that Sx = 1/2*(S+ + S-) and measure things like <S+_i S-_j> instead.

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