I have been trying to calculate the dynamics of bosons recently. And I need to represent the ground state and excited state of bosons separately through appropriate matching. For example, a simple example:

```
L = 2
tₜₒₜₐₗ = 10
τ = 0.01
tₛₜₑₚₛ = convert(Int64, tₜₒₜₐₗ /τ)
sites = siteinds("Boson",2L)
states = ["1","0","0","1"]
ψ₀ = MPS(sites,states)
os = OpSum()
for i in 1:2L
os += "a†",i
os += "a",i
end
ℋ = MPO(os,sites)
ψₜ = ψ₀
N̂ₛₜₑₚₛ = []
for i in 1:tₛₜₑₚₛ
N̂ = expect(ψₜ ,"N")
push!(N̂ₛₜₑₚₛ ,N̂')
ψₜ = tdvp(ℋ,ψₜ ,-im*τ,ishermitian=false; nsite=2)
end
```

This example shows that we have a total of two bosons, and using siteinds, we set the first two sites to represent the ground state of the boson, and the last two sites to represent the excited state of the boson. In this way, my initial state is set as the first boson in the ground state and the second boson in the excited state. When I performed time-dependent evolution on it, the particle population image obtained was as I expected.

But when I changed ‘siteinds’ to

```
sites = siteinds("Boson",2L; conserve_qns=true)
```

Instead, there is a situation where the number of bosons is not conserved

So my question is, according to my settings, how can I ensure that the number of bosons is conserved?

Because when I was calculating other Hamiltonians, I encountered a situation where the expected sum of the number of particles at all sites was not conserved. In this case, an error will be reported

```
Eigen currently only supports block diagonal matrices.
Stacktrace:
[1] error(s::String)
@ Base .\error.jl:35
[2] eigen(T::Hermitian{ComplexF64, NDTensors.BlockSparseTensor{ComplexF64, 2, Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}, NDTensors.BlockSparse{ComplexF64, Vector{ComplexF64}, 2}}}; min_blockdim::Nothing, mindim::Int64, maxdim::Int64, cutoff::Float64, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing)
@ NDTensors C:\Users\15935\.julia\packages\NDTensors\RDn3T\src\blocksparse\linearalgebra.jl:227
[3] eigen(A::ITensor, Linds::Vector{Index{Vector{Pair{QN, Int64}}}}, Rinds::Vector{Index{Vector{Pair{QN, Int64}}}}; mindim::Int64, maxdim::Int64, cutoff::Float64, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing, ishermitian::Bool, tags::TagSet, lefttags::Nothing, righttags::Nothing, plev::Nothing, leftplev::Nothing, rightplev::Nothing)
@ ITensors C:\Users\15935\.julia\packages\ITensors\MnaxI\src\tensor_operations\matrix_decomposition.jl:378
[4] factorize_eigen(A::ITensor, Linds::Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}; ortho::String, eigen_perturbation::Nothing, mindim::Int64, maxdim::Int64, cutoff::Float64, tags::TagSet)
@ ITensors C:\Users\15935\.julia\packages\ITensors\MnaxI\src\tensor_operations\matrix_decomposition.jl:672
[5] factorize(A::ITensor, Linds::Tuple{Index{Vector{Pair{QN, Int64}}}, Index{Vector{Pair{QN, Int64}}}}; mindim::Int64, maxdim::Int64, cutoff::Float64, ortho::String, tags::TagSet, plev::Nothing, which_decomp::Nothing, eigen_perturbation::Nothing, svd_alg::String, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing, min_blockdim::Nothing, singular_values!::Nothing, dir::Nothing)
@ ITensors C:\Users\15935\.julia\packages\ITensors\MnaxI\src\tensor_operations\matrix_decomposition.jl:790
[6] replacebond!(M::MPS, b::Int64, phi::ITensor; normalize::Bool, swapsites::Nothing, ortho::String, which_decomp::Nothing, mindim::Int64, maxdim::Int64, cutoff::Float64, eigen_perturbation::Nothing, svd_alg::String)
@ ITensors C:\Users\15935\.julia\packages\ITensors\MnaxI\src\mps\mps.jl:555
[7] tdvp_site_update!(nsite_val::Val{2}, reverse_step_val::Val{true}, solver::ITensorTDVP.var"#solver#34"{ITensorTDVP.var"#solver#33#35"{Base.Pairs{Symbol, Real, NTuple{6, Symbol}, NamedTuple{(:ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite), Tuple{Bool, Bool, Int64, Int64, Float64, Int64}}}}}, PH::ProjMPO, psi::MPS, b::Int64; current_time::Float64, outputlevel::Int64, time_step::ComplexF64, normalize::Bool, direction::Base.Order.ForwardOrdering, noise::Float64, which_decomp::Nothing, svd_alg::String, cutoff::Float64, maxdim::Int64, mindim::Int64, maxtruncerr::Float64)
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_step.jl:365
[8] tdvp_site_update!(solver::ITensorTDVP.var"#solver#34"{ITensorTDVP.var"#solver#33#35"{Base.Pairs{Symbol, Real, NTuple{6, Symbol}, NamedTuple{(:ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite), Tuple{Bool, Bool, Int64, Int64, Float64, Int64}}}}}, PH::ProjMPO, psi::MPS, b::Int64; nsite::Int64, reverse_step::Bool, current_time::Float64, outputlevel::Int64, time_step::ComplexF64, normalize::Bool, direction::Base.Order.ForwardOrdering, noise::Float64, which_decomp::Nothing, svd_alg::String, cutoff::Float64, maxdim::Int64, mindim::Int64, maxtruncerr::Float64)
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_step.jl:157
[9] tdvp_sweep(direction::Base.Order.ForwardOrdering, solver::Function, PH::ProjMPO, time_step::ComplexF64, psi::MPS; kwargs::Base.Pairs{Symbol, Real, NTuple{11, Symbol}, NamedTuple{(:current_time, :ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite, :reverse_step, :sweep, :mindim, :noise), Tuple{Float64, Bool, Bool, Int64, Int64, Float64, Int64, Bool, Int64, Int64, Float64}}})
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_step.jl:80
[10] tdvp_step(order::ITensorTDVP.TDVPOrder{2, Base.Order.ForwardOrdering()}, solver::Function, PH::ProjMPO, time_step::ComplexF64, psi::MPS; current_time::Float64, kwargs::Base.Pairs{Symbol, Real, NTuple{10, Symbol}, NamedTuple{(:ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite, :reverse_step, :sweep, :mindim, :noise), Tuple{Bool, Bool, Int64, Int64, Float64, Int64, Bool, Int64, Int64, Float64}}})
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_step.jl:9
[11] macro expansion
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_generic.jl:84 [inlined]
[12] macro expansion
@ .\timing.jl:393 [inlined]
[13] tdvp(solver::Function, PH::ProjMPO, t::ComplexF64, psi0::MPS; kwargs::Base.Pairs{Symbol, Real, NTuple{6, Symbol}, NamedTuple{(:ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite), Tuple{Bool, Bool, Int64, Int64, Float64, Int64}}})
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_generic.jl:83
[14] tdvp
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_generic.jl:45 [inlined]
[15] tdvp(solver::Function, H::MPO, t::ComplexF64, psi0::MPS; kwargs::Base.Pairs{Symbol, Real, NTuple{6, Symbol}, NamedTuple{(:ishermitian, :normalize, :sweeps, :maxdim, :cutoff, :nsite), Tuple{Bool, Bool, Int64, Int64, Float64, Int64}}})
@ ITensorTDVP C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_generic.jl:150
[16] tdvp
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp_generic.jl:143 [inlined]
[17] #tdvp#41
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp.jl:47 [inlined]
[18] tdvp
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp.jl:46 [inlined]
[19] #tdvp#43
@ C:\Users\15935\.julia\packages\ITensorTDVP\V1Kco\src\tdvp.jl:55 [inlined]
[20] macro expansion
@ .\In[63]:10 [inlined]
[21] top-level scope
@ .\timing.jl:273 [inlined]
[22] top-level scope
@ .\In[63]:0
```

I am very much looking forward to receiving any form of help, and would greatly appreciate it if there is one！