Applying projective operator to MPS

Question

In the iTensor documentation, a default projective operator is mentioned, with the example code

auto sites = SpinHalf(N);
//Projects site 3 onto state 2 (i.e. the down state)
auto P3_2 = op(sites,"Proj",3,{"State",2});

However, I'm confused as to what form this operator is in, and how it can be actually applied to a spin-half MPS. Treating P3_2 as an MPO and running applyMPO(P3_2, psi) gives an error, as are my attempts to package P3_2 into an AutoMPO object somehow. What does the intended usage of these operators look like?

Answer 1

Hi,

You would apply it by contracting it with an MPS that has the indices sites, i.e.:

psi(3) *= P3_2;
psi(3).noPrime();  // To make the site index unprimed again

It can help to print objects that you are unsure about, for example with:

PrintData(P3_2);

you can see that it is an ITensor with a pair of unprimed and primed indices.

-Matt