Jordan wigner fermi string in self-writing AutoMPO

Question

I'm working on a 3-flavor fermion model on DMRG and coming up with the correlation of fermion operator.
I don't know the rule of Jordan Wigner string "F" in this situation. Please give me some info about how AutoMPO deal with self-writing Fermions

Answer 1

Hello,

Thanks for the question. Have you taken a look at this tutorial page on Jordan-Wigner strings and fermions? https://itensor.org/docs.cgi?page=tutorials/fermions

AutoMPO will basically use the rules outlined on that page to generate the Jordan-Wigner strings, that should give you an idea for how it works.

-Matt

Answer 2

Matt's answer is the right one, and do please see that article about fermions and how they are handled in ITensor.

To provide some additional information, there is currently only one place in ITensor where fermions are handled automatically for you, and that is in the AutoMPO system. So if you input Hamiltonian terms which contain fermionic operators (such as C and Cdag for spinless fermions, or Cup, Cdagup, Cdn, Cdagdn for electrons) then the AutoMPO system will use special rewriting rules and insert Jordan-Wigner string for you. (In the Julia version of ITensor, you can also extend this system for custom physical site types.) So the resulting MPO will be guaranteed to be correct in terms of treating fermionic operators.

On the other hand, when working with an MPS such as the one obtained after a DMRG calculation, you must insert Jordan-Wigner string operators yourself when measuring fermionic correlation functions, such as between a c-dagger and c operator acting on spatially separated sites. We have an example of how to do this for spinless fermions in the C++ version linked here:
http://itensor.org/docs.cgi?vers=cppv3&page=formulas/spinless_correlator_mps

Hope that helps -

Miles