So here is the output that I get:

MPS:

ITensor ord=2:

(4|id=238|n=1,Elec,Site) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=559|U,Link) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.00 (QDense Real)}

ITensor ord=2:

(4|id=559|U,Link) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=233|n=2,Elec,Site) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=1.00 (QDense Real)}

ITensor ord=2:

(4|id=573|n=3,Elec,Site) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=320|U,Link) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.00 (QDense Real)}

ITensor ord=2:

(4|id=320|U,Link) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=258|n=4,Elec,Site) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=1.00 (QDense Real)}

-----------------

I think the MPS looks fine to me.

-------------------------------

MPO, which is the Cdagup, 1, Cup, 2:

ITensor ord=3:

(3|id=279|l=1,Link) <Out>

1: 2 QN()

2: 1 QN({"Nf",-1,-1},{"Sz",1})

(4|id=238|n=1,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=238|n=1,Elec,Site) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.45 (QDense Real)}

ITensor ord=4:

(3|id=279|l=1,Link) <In>

1: 2 QN()

2: 1 QN({"Nf",-1,-1},{"Sz",1})

(2|id=165|l=2,Link) <Out>

1: 2 QN()

(4|id=233|n=2,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=233|n=2,Elec,Site) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=3.16 (QDense Real)}

ITensor ord=4:

(2|id=165|l=2,Link) <In>

1: 2 QN()

(2|id=616|l=3,Link) <Out>

1: 2 QN()

(4|id=573|n=3,Elec,Site) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=573|n=3,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.83 (QDense Real)}

ITensor ord=3:

(2|id=616|l=3,Link) <In>

1: 2 QN()

(4|id=258|n=4,Elec,Site) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=258|n=4,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.00 (QDense Real)}

-----------------

What do you think of that?

--------------------------

And lastly, the MPO acting on the MPS:

ITensor ord=2:

(2|id=275|U,Link) <Out>

1: 1 QN({"Nf",2,-1},{"Sz",0})

2: 1 QN({"Nf",3,-1},{"Sz",1})

(4|id=238|n=1,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=0.71 (QDense Real)}

ITensor ord=3:

(1|id=373) <Out>

1: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=233|n=2,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(2|id=275|U,Link) <In>

1: 1 QN({"Nf",2,-1},{"Sz",0})

2: 1 QN({"Nf",3,-1},{"Sz",1})

{norm=1.41 (QDense Real)}

ITensor ord=3:

(4|id=985|U,Link) <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=573|n=3,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(1|id=373) <In>

1: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=1.00 (QDense Real)}

ITensor ord=2:

(4|id=258|n=4,Elec,Site)' <Out>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

(4|id=985|U,Link) <In>

1: 1 QN({"Nf",0,-1},{"Sz",0})

2: 1 QN({"Nf",1,-1},{"Sz",1})

3: 1 QN({"Nf",1,-1},{"Sz",-1})

4: 1 QN({"Nf",2,-1},{"Sz",0})

{norm=2.00 (QDense Real)}

----------------------

There is something in the 3rd iTensor that doesn't look right to me...

What do you think?