Value of the operator "Sz" returned by totalQN for Hubbard site set?

Question

I am a little bit confused about the value for Sz which is returned by the function totalQN for a spin-imbalanced Hubbard model.
If I put a single spin up on the lattice, totalQN returns the value Sz=1, whereas I would expect a contribution of +/-0.5 per spin up/down.

Answer 1

Hi, good question. Our QN (quantum number) objects deal with integers only for efficiency and space reasons. So we work in units of spin half, i.e. a quantum number of 1 means Sz=0.5, 2 means Sz=1.0, etc.

It's a computer representation/efficiency versus physics thing.

I should have put this on the documentation page for the QN system, so I just updated that page with more info:

http://itensor.org/docs.cgi?page=classes/qn

Comments

Hello, Miles.
Thanks for your quick reply (and for all the work you're putting into ITensor!)
Actually I haven't looked at the page for the QN system yet, thanks for pointing it out.
You might also want to change the page for the Hubbard class? It's written there: "the z-component spin operator (+0.5 for an up spin, -0.5 for a down spin)", that's what got me confused in the first place.

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Hi Michael, the comment on the Hubbard page was referring to the matrix elements of the Sz operator versus a total Sz quantum number, so the matrix elements of the operator are indeed 0.5 and -0.5. But I'll add the phrase "matrix elements" there so people know that's what I was referring to - thanks.