# Errors in TDVP function

**URL:** <https://itensor.discourse.group/t/errors-in-tdvp-function/907>\
**Category:** DMRG and Numerical Methods\
**Tags:** julia, mps\
**Created:** [May 31, 2023, 5:50pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907 "2023-05-31T17:50:05Z")\
**Posts on this page:** 11\
**Page:** 1

<div class="post-metadata">

**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [May 31, 2023, 5:50pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/1 "2023-05-31T17:50:05Z")

</div>

Hey all,

I am trying to implement the TDVP function, and I get some weird error that I couldn’t figure out what is the reason.

Basically, I am trying the develop in imaginary time the following wave function

|\psi\_0 \rangle = |0...0\rangle \\ |\psi \rangle= \frac{e^{-\beta H}|\psi\_0 \rangle}{ |\langle \psi| \psi \rangle|}

And for some reason I am getting a “InexactError”.  
Can someone help me out understand this ?

some example:

```auto
n=3 
site=siteinds("Qubit",n)
psi=MPS(site, n->"Up")
tau=0.1 
for I=1:20
    psi=tdvp(H_bath,psi,-τ;cutoff=1e-28)
    normalize!(psi)
end

```

H is some Hamiltonian that describes long-ranged interactions.

For local Hamiltonian there is no error.

I will also add the error in case it will help…  
Thanks a lot in advance!

The error is:

```auto
ERROR: LoadError: InexactError: Float64(0.5734939687060105 + 2.90389650522495e-17im)
Stacktrace:
  [1] Real
    @ ./complex.jl:44 [inlined]
  [2] convert
    @ ./number.jl:7 [inlined]
  [3] setindex!(::Matrix{Float64}, ::ComplexF64, ::Int64, ::Int64)
    @ Base ./array.jl:905
  [4] applyexp(H::ProjMPO, tau::Float64, x0::ITensor; kwargs::Base.Pairs{Symbol, Real, NTuple{4, Symbol}, NamedTuple{(:tol, :maxiter, :outputlevel, :current_time), Tuple{Float64, Int64, Int64, Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/applyexp.jl:54
  [5] (::ITensorTDVP.var"#solver#38"{ITensorTDVP.var"#solver#37#39"{Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}}}})(H::ProjMPO, t::Float64, psi0::ITensor; kws::Base.Pairs{Symbol, Real, Tuple{Symbol, Symbol}, NamedTuple{(:current_time, :outputlevel), Tuple{Float64, Int64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp.jl:27
  [6] tdvp_site_update!(nsite_val::Val{2}, reverse_step_val::Val{true}, solver::ITensorTDVP.var"#solver#38"{ITensorTDVP.var"#solver#37#39"{Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}}}}, PH::ProjMPO, psi::MPS, b::Int64; current_time::Float64, outputlevel::Int64, time_step::Float64, normalize::Bool, direction::Base.Order.ForwardOrdering, noise::Float64, which_decomp::Nothing, svd_alg::String, cutoff::Float64, maxdim::Int64, mindim::Int64, maxtruncerr::Float64)
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_step.jl:356
  [7] tdvp_site_update!(solver::ITensorTDVP.var"#solver#38"{ITensorTDVP.var"#solver#37#39"{Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}}}}, PH::ProjMPO, psi::MPS, b::Int64; nsite::Int64, reverse_step::Bool, current_time::Float64, outputlevel::Int64, time_step::Float64, normalize::Bool, direction::Base.Order.ForwardOrdering, noise::Float64, which_decomp::Nothing, svd_alg::String, cutoff::Float64, maxdim::Int64, mindim::Int64, maxtruncerr::Float64)
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_step.jl:157
  [8] tdvp_sweep(direction::Base.Order.ForwardOrdering, solver::Function, PH::ProjMPO, time_step::Float64, psi::MPS; kwargs::Base.Pairs{Symbol, Real, NTuple{7, Symbol}, NamedTuple{(:current_time, :cutoff, :reverse_step, :sweep, :maxdim, :mindim, :noise), Tuple{Float64, Float64, Bool, Int64, Int64, Int64, Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_step.jl:80
  [9] tdvp_step(order::ITensorTDVP.TDVPOrder{2, Base.Order.ForwardOrdering()}, solver::Function, PH::ProjMPO, time_step::Float64, psi::MPS; current_time::Float64, kwargs::Base.Pairs{Symbol, Real, NTuple{6, Symbol}, NamedTuple{(:cutoff, :reverse_step, :sweep, :maxdim, :mindim, :noise), Tuple{Float64, Bool, Int64, Int64, Int64, Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_step.jl:9
 [10] macro expansion
    @ ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_generic.jl:84 [inlined]
 [11] macro expansion
    @ ./timing.jl:299 [inlined]
 [12] tdvp(solver::Function, PH::ProjMPO, t::Float64, psi0::MPS; kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_generic.jl:83
 [13] tdvp(solver::Function, H::MPO, t::Float64, psi0::MPS; kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp_generic.jl:150
 [14] tdvp(H::MPO, t::Float64, psi0::MPS; kwargs::Base.Pairs{Symbol, Float64, Tuple{Symbol}, NamedTuple{(:cutoff,), Tuple{Float64}}})
    @ ITensorTDVP ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp.jl:47
 [15] #tdvp#43
    @ ~/.julia/packages/ITensorTDVP/c3OYY/src/tdvp.jl:55 [inlined]
 [16] top-level scope
    @ ~/Desktop/projects/Density_matrix/Decoherence/Energy_density.jl:72
in expression starting at /home/Tomer/Desktop/projects/Density_matrix/Decoherence/Energy_density.jl:70

```

---

<div class="post-metadata">

**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [May 31, 2023, 5:53pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/2 "2023-05-31T17:53:42Z")

</div>

Is the Hamiltonian complex?

---

<div class="post-metadata">

**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [May 31, 2023, 6:15pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/3 "2023-05-31T18:15:47Z")

</div>

Hey,  
No.  
If you wish I can share it here

---

<div class="post-metadata">

**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [June 1, 2023, 12:22am UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/4 "2023-06-01T00:22:45Z")

</div>

Yeah, please share a full minimal example that reproduces that bug. It’s not clear to me why a complex number would be showing up, it may be an issue with the `applyexp` solver backend. As an alternative you could try the `exponentiate` backend, which makes use of KrylovKit.jl, by passing the keyword argument `solver_backend="exponentiate"`.

---

<div class="post-metadata">

**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [June 1, 2023, 6:30am UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/5 "2023-06-01T06:30:05Z")

</div>

Hey,  
Sorry for the mistake. The Hamiltonian includes the “Sy” operator, but when I applied only “Sy”, it did not printed an error.

The Hamiltonian:

```auto
    J=randn(n,n,3,3)
    os = OpSum()
    A = ["Sx", "Sy", "Sz"]
    for j in 1:n-1
        for i in j+1:n
            for α in 1:3
                for β in 1:3
                    os += J[i,j,α,β], A[α], i, A[β], j
                end
            end
        end
    end
    H_syk = MPO(os, site)

```

I hope it will help.

---

<div class="post-metadata">

**Author:** ![miles](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/miles/32/6_2.png) [@miles](https://itensor.discourse.group/u/miles)\
**Post date:** [June 1, 2023, 1:18pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/6 "2023-06-01T13:18:15Z")

</div>

I think here it might solve your problem to rewrite your Hamiltonian in terms of the “S+” and “S-” operators instead of “Sy” and “Sx”. This is because “S+” and “S-” are real-valued so you would not encounter any complex numbers that way.

---

<div class="post-metadata">

**Author:** ![tsegev](https://avatars.discourse-cdn.com/v4/letter/t/5e9695/32.png) [@tsegev](https://itensor.discourse.group/u/tsegev)\
**Post date:** [June 1, 2023, 2:00pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/7 "2023-06-01T14:00:06Z")

</div>

Hey miles!  
thank you for your comment. I will try that

---

<div class="post-metadata">

**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [June 1, 2023, 6:38pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/8 "2023-06-01T18:38:35Z")

</div>

Related issue: [Fix complex issue in applyexp solver · Issue #49 · ITensor/ITensorTDVP.jl · GitHub](https://github.com/ITensor/ITensorTDVP.jl/issues/49) and discourse thread: [tdvp time developing](https://itensor.discourse.group/t/tdvp-time-developing/563)

---

<div class="post-metadata">

**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [June 1, 2023, 6:39pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/9 "2023-06-01T18:39:53Z")

</div>

When it rains, it pours: [TDVP for a Hamiltonian with complex parameters](https://itensor.discourse.group/t/tdvp-for-a-hamiltonian-with-complex-parameters/909)

---

<div class="post-metadata">

**Author:** ![mtfishman](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/mtfishman/32/11_2.png) [@mtfishman](https://itensor.discourse.group/u/mtfishman)\
**Post date:** [June 1, 2023, 6:41pm UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/10 "2023-06-01T18:41:05Z")

</div>

@miles we should probably just change the default backend to `"exponentiate"`.

---

<div class="post-metadata">

**Author:** ![ZhiguangLu](https://yyz2.discourse-cdn.com/free1/user_avatar/itensor.discourse.group/zhiguanglu/32/172_2.png) [@ZhiguangLu](https://itensor.discourse.group/u/ZhiguangLu)\
**Post date:** [June 6, 2023, 11:14am UTC](https://itensor.discourse.group/t/errors-in-tdvp-function/907/11 "2023-06-06T11:14:44Z")

</div>

I have been met the problem, and you just need a command to solve it, i.e,

MPS(ComplexF64, s)