Hi,

Here is my Hamiltonian with Majorana operator @@\lambda^1=C+C^\dagger@@ :

```
auto sites = Spinless(N,{"ConserveNf",false});
// Create the Hamiltonian using AutoMPO
auto ampo = AutoMPO(sites);
for(int i = 1; i <= N; ++i)
{
ampo += -1.0,"C",i;
ampo += -1.0,"Cdag",i;
}
```

For N=2, the Hamiltonian should be

$$

\begin{pmatrix}

0 & -1 & -1 & 0\\

-1 & 0 & 0 & -1\\

-1 & 0 & 0 & -1\\

0 & -1& -1 & 0\\

\end{pmatrix}

$$

However, the ITensor of H is

ITensor r=4: ("Spinless 1",2,Site|578)' ("Spinless 1",2,Site|578) ("Spinless 2",2,Site|138)' ("Spinless 2",2,Site|138)

{log(scale)=1.04, norm=2.83 (Dense Real)}

(2,1,1,1) -1.000000

(1,2,1,1) 1.0000000

(1,1,2,1) -1.000000

(2,2,2,1) -1.000000

(1,1,1,2) 1.0000000

(2,2,1,2) 1.0000000

(2,1,2,2) -1.000000

(1,2,2,2) 1.0000000

which is

$$

\begin{pmatrix}

0 & 1 & 1 & 0\\

-1 & 0 & 0 & 1\\

-1 & 0 & 0 & 1\\

0 & -1& -1 & 0\\

\end{pmatrix}

$$

is not Hermitian but DMRG reported energy is

Energy after sweep 6/6 is -2.000000000000

Using overlap <G|H|G> = -0.0000000000

The ground state |G> is

ITensor r=2: ("Spinless 1",2,Site|578) ("Spinless 2",2,Site|138)

{log(scale)=-0.00, norm=1.00 (Dense Real)}

(1,1) 1.0000000

which is |00>

In short, the Autompo seems not working on such @@Hamitonian = C_i + C^\dagger_i@@

Moreover, by using A and F operators instead for two sites,

```
ampo += -1,"A",1;
ampo += -1,"Adag",1;
ampo += -1,"F",1,"A",2;
ampo += -1,"F",1,"Adag",2;
```

Energy after sweep 6/6 is -1.414213562373

Using overlap = -1.4142135624

ITensor r=4: ("Spinless 1",2,Site|28) ("Spinless 1",2,Site|28)' ("Spinless 2",2,Site|438) ("Spinless 2",2,Site|438)'

{log(scale)=1.04, norm=2.83 (Dense Real)}

(2,1,1,1) -1.000000

(1,2,1,1) -1.000000

(1,1,2,1) -1.000000

(2,2,2,1) 1.0000000

(1,1,1,2) -1.000000

(2,2,1,2) 1.0000000

(2,1,2,2) -1.000000

(1,2,2,2) -1.000000

which is

$$

\begin{pmatrix}

0 & -1 & -1 & 0\\

-1 & 0 & 0 & -1\\

-1 & 0 & 0 & 1\\

0 & -1& 1 & 0\\

\end{pmatrix}

$$

and it's still not correct.

Could you help me out with it?

Thanks.

Best,

Victor