[ITensors] [BUG] Autofermion system incompatible with simple (no QN) Indices (when factorizing)

[b-kloss]

Description of bug

Enabling the Autofermion system (ITensors.enable_auto_fermion) leads to errors when performing DMRG on a system without quantum number conservation enforced.

Minimal code demonstrating the bug or unexpected behavior

This is a copy of examples/dmrg/1d_heisenberg.jl up to ITensors.enable_auto_fermion() at the top of the code block.

Minimal runnable code

using ITensors
using Printf
using Random

Random.seed!(1234)

let
  N = 100
  ITensors.enable_auto_fermion()
  # Create N spin-one degrees of freedom
  sites = siteinds("S=1", N)
  # Alternatively can make spin-half sites instead
  #sites = siteinds("S=1/2", N)

  # Input operator terms which define a Hamiltonian
  os = OpSum()
  for j in 1:(N - 1)
    os += "Sz", j, "Sz", j + 1
    os += 0.5, "S+", j, "S-", j + 1
    os += 0.5, "S-", j, "S+", j + 1
  end
  # Convert these terms to an MPO tensor network
  H = MPO(os, sites)

  # Create an initial random matrix product state
  psi0 = randomMPS(sites; linkdims=10)

  # Plan to do 5 DMRG sweeps:
  nsweeps = 5
  # Set maximum MPS bond dimensions for each sweep
  maxdim = [10, 20, 100, 100, 200]
  # Set maximum truncation error allowed when adapting bond dimensions
  cutoff = [1E-11]

  # Run the DMRG algorithm, returning energy and optimized MPS
  energy, psi = dmrg(H, psi0; nsweeps, maxdim, cutoff)
  @printf("Final energy = %.12f\n", energy)
end

Expected output or behavior

DMRG should run successfully.

Actual output or behavior An error is raised in the factorization, regarding the expected arrow-directions when the autofermion system is enabled. I expect the solution to be change the default arrow-direction when either interpreting a non-QN Index as a QNIndex with trivial QN or converting one to the other.

Output of minimal runnable code

ERROR: LoadError: With auto_fermion enabled, left inds in eigen must have Out arrows
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] eigen(A::ITensor, Linds::Vector{Index{Int64}}, Rinds::Vector{Index{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 ~/.julia/v1.9/packages/ITensors/Gf9aD/src/tensor_operations/matrix_decomposition.jl:358
  [3] factorize_eigen(A::ITensor, Linds::Tuple{Index{Int64}, Index{Int64}}; ortho::String, eigen_perturbation::Nothing, mindim::Int64, maxdim::Int64, cutoff::Float64, tags::TagSet, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing)
    @ ITensors ~/.julia/v1.9/packages/ITensors/Gf9aD/src/tensor_operations/matrix_decomposition.jl:680
  [4] factorize(A::ITensor, Linds::Tuple{Index{Int64}, Index{Int64}}; mindim::Int64, maxdim::Int64, cutoff::Float64, ortho::String, tags::TagSet, plev::Nothing, which_decomp::Nothing, eigen_perturbation::Nothing, svd_alg::Nothing, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing, min_blockdim::Nothing, singular_values!::Nothing, dir::Nothing)
    @ ITensors ~/.julia/v1.9/packages/ITensors/Gf9aD/src/tensor_operations/matrix_decomposition.jl:827
  [5] 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::Nothing, use_absolute_cutoff::Nothing, use_relative_cutoff::Nothing, min_blockdim::Nothing)
    @ ITensors ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/mps.jl:559
  [6] replacebond!
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/mps.jl:530 [inlined]
  [7] #replacebond!#956
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/mps.jl:606 [inlined]
  [8] macro expansion
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:277 [inlined]
  [9] macro expansion
    @ ~/.julia/v1.9/packages/TimerOutputs/RsWnF/src/TimerOutput.jl:253 [inlined]
 [10] macro expansion
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:276 [inlined]
 [11] macro expansion
    @ ./timing.jl:393 [inlined]
 [12] dmrg(PH::ProjMPO, psi0::MPS, sweeps::Sweeps; which_decomp::Nothing, svd_alg::Nothing, observer::NoObserver, outputlevel::Int64, write_when_maxdim_exceeds::Nothing, write_path::String, eigsolve_tol::Float64, eigsolve_krylovdim::Int64, eigsolve_maxiter::Int64, eigsolve_verbosity::Int64, eigsolve_which_eigenvalue::Symbol, ishermitian::Bool)
    @ ITensors ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:204
 [13] dmrg
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:156 [inlined]
 [14] #dmrg#1053
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:27 [inlined]
 [15] dmrg
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:20 [inlined]
 [16] #dmrg#1059
    @ ~/.julia/v1.9/packages/ITensors/Gf9aD/src/mps/dmrg.jl:391 [inlined]
 [17] top-level scope
    @ ~/.julia/v1.9/dev/ITensors/examples/dmrg/1d_heisenberg_af.jl:36
 [18] include(fname::String)
    @ Base.MainInclude ./client.jl:478
 [19] top-level scope
    @ REPL[3]:1
in expression starting at /mnt/home/bkloss/.julia/v1.9/dev/ITensors/examples/dmrg/1d_heisenberg_af.jl:7

Version information

• Output from versioninfo():

julia> versioninfo()
Commit 8e63055292* (2023-05-07 11:25 UTC)
Platform Info:
  OS: Linux (x86_64-pc-linux-gnu)
  CPU: 32 × Intel(R) Xeon(R) Gold 6234 CPU @ 3.30GHz
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-14.0.6 (ORCJIT, cascadelake)
  Threads: 1 on 32 virtual cores

• Output from using Pkg; Pkg.status("ITensors"):

julia> using Pkg; Pkg.status("ITensors")
Status `~/projects/ITensors_issues/af_vs_noqn/Project.toml`
  [9136182c] ITensors v0.3.54

[mtfishman]

@emstoudenmire could you take a look?

[mtfishman]

Closed by #1380.