How to handle with 1-D Bose-Fermi mixture by using DMRG with iTensor

Question

Hello, I'm currently considering a 1-D Bose-Fermi spinor mixture system, in which fermion is spin-1/2 and boson is spin-1 and soft(not hard core).

I have noticed this nice answer: http://itensor.org/support/118/constructing-sites-chain-alternating-bosonic-degrees-freedom which consider a similar question. Is this strategy also applicable for my problems ? That is, I just need to write my own SiteSet file to define the lattice model I consider. Nothing needs to be changed to AutoMPO and MPO or DMRG function itself when I construct my Hamiltonian and do the calculation.

By the way, is there any other way to construct this 1-D B-F mixture ? For example, we may treat this 1-D lattice as a connected 1-D ladder with one of this being spin-1 and other being spin-1/2, just as the example given in the tutorial of iTensor.

Thanks ! PS: iTensor is really a fascinating MPS library with simple data structure.

Answer 1

Thanks for the kind words. The good news is that all you need is a custom site set and then all of the other parts of the code (such as AutoMPO, MPO, DMRG) should just automatically work. I recently made a site set for a student who is doing a two-leg ladder setup like you suggested where each leg has a different type of quantum number. If you email me I can send you the source code for this site set for you to use as an example.

To deal with fermions specifically, things might get a bit tricky with AutoMPO. We'd probably have to talk about how to deal with it best. But I think it could work ok. Basically you'd have to define a fermion string operator called "F" for both fermion and boson sites, and just define it to be a trivial identity operator for the fermion sites.

Ultimately this would be a good type of SiteSet to add to ITensor.

Miles