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asked by (220 points)

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.

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answered by (70.1k points)
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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:


commented by (220 points)
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.
commented by (70.1k points)
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.
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