[ITensors] [BUG] exp(A::ITensor) not working with auto_fermion

[JoeyT1994]

When you enable auto_fermion, i.e. ITensors.enable_auto_fermion() then exp(A::ITensor) doesn't return the correct result.

Here is a minimal working example just building the identity matrix with exp (but the incorrect result propagates to exponentiating more complicated ITensors) and comparing to the correct result.

Minimal runnable code

using ITensors

ITensors.enable_auto_fermion()

n = 4
s = siteinds("Fermion", n; conserve_qns=true)

id_tensor = op("I", s[2])*op("I", s[3])
@show id_tensor


id_tensor_from_exp = exp(0.0 * id_tensor)
@show permute(id_tensor_from_exp, inds(id_tensor))

@show id_tensor == id_tensor_from_exp

Both of these methods should return the same, identity matrix but the one returned from exp is not (which you can check by applying it to a wavefunction) and has signs which are wrong.

Output of minimal runnable code

id_tensor = ITensor ord=4
Dim 1: (dim=2|id=147|"Fermion,Site,n=2")' <Out>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 2: (dim=2|id=147|"Fermion,Site,n=2") <In>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 3: (dim=2|id=164|"Fermion,Site,n=3")' <Out>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 4: (dim=2|id=164|"Fermion,Site,n=3") <In>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
NDTensors.BlockSparse{Float64, Vector{Float64}, 4}
 2×2×2×2
Block(1, 1, 1, 1)
 [1:1, 1:1, 1:1, 1:1]
[:, :, 1, 1] =
 1.0

Block(1, 1, 2, 2)
 [1:1, 1:1, 2:2, 2:2]
[:, :, 1, 1] =
 1.0

Block(2, 2, 1, 1)
 [2:2, 2:2, 1:1, 1:1]
[:, :, 1, 1] =
 1.0

Block(2, 2, 2, 2)
 [2:2, 2:2, 2:2, 2:2]
[:, :, 1, 1] =
 1.0
permute(id_tensor_from_exp, inds(id_tensor)) = ITensor ord=4
Dim 1: (dim=2|id=147|"Fermion,Site,n=2")' <Out>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 2: (dim=2|id=147|"Fermion,Site,n=2") <In>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 3: (dim=2|id=164|"Fermion,Site,n=3")' <Out>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
Dim 4: (dim=2|id=164|"Fermion,Site,n=3") <In>
 1: QN("Nf",0,-1) => 1
 2: QN("Nf",1,-1) => 1
NDTensors.BlockSparse{Float64, Vector{Float64}, 4}
 2×2×2×2
Block(1, 1, 1, 1)
 [1:1, 1:1, 1:1, 1:1]
[:, :, 1, 1] =
 1.0

Block(2, 2, 1, 1)
 [2:2, 2:2, 1:1, 1:1]
[:, :, 1, 1] =
 -1.0

Block(1, 2, 2, 1)
 [1:1, 2:2, 2:2, 1:1]
[:, :, 1, 1] =
 0.0

Block(2, 1, 1, 2)
 [2:2, 1:1, 1:1, 2:2]
[:, :, 1, 1] =
 -0.0

Block(1, 1, 2, 2)
 [1:1, 1:1, 2:2, 2:2]
[:, :, 1, 1] =
 -1.0

Block(2, 2, 2, 2)
 [2:2, 2:2, 2:2, 2:2]
[:, :, 1, 1] =
 -1.0
id_tensor == id_tensor_from_exp = false