+1 vote
asked by (130 points)

Hello,
I would like to use three (or more) body operators in the time evolution, using the expH method (either exact and fit apply). However, I get the error message that this is not supported.
For DMRG methods, however, many-body operators work fine.
My question is: How can one do time evolution with three (or more) body operators?
I can see from the code that Jordan-Wigner strings are already implemented, which are a type of many-body operators.
Is there a way to add general many-body operators? In particular, I would like to add generalized Jordan-Wigner strings (for anyons).
Any help would be appreciated.

Kind regards
Tobias Haug

1 Answer

0 votes
answered by (28.2k points)

Hi Tobias,
Thanks for the question. The short answer is just that the toExpH function just doesn't support operators beyond two-site operators at the moment, even though the non-exponentiated part of AutoMPO does support it. This is a fixable feature, but I may not find time to fix it very soon. Since another user also asked about it recently, though, I'll try to prioritize adding it in.

But in the mean time, another approach to time evolving with arbitrary Hamiltonians is to use the "time step targeting" method which is very similar to the "TDVP" method of Haegeman and Verstraete. Here are two papers on the time-step targeting method:

https://arxiv.org/abs/cond-mat/0502475

https://arxiv.org/abs/1706.09537

We don't have this method implemented in ITensor, but ITensor would be very well suited for writing your own implementation.

Regarding more generalized Jordan-Wigner string, that's not something I could quickly add to AutoMPO. You are welcome to look at how fermion J-W string gets handled in AutoMPO and make your own modified version for your system, but instead of adding all of the different cases people might try on top of what is a rather temporary solution that we have currently, I am working instead to overhaul our approach to fermions and non-Abelian anyons.

The new approach I'm working on actually makes certain types of IQIndex objects anticommute (or commute up to a general phase factor) when in certain QN sectors. It will take until at least this fall for this feature to be put in, though, and no guarantee it will work as well as I'm hoping -

Miles

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