Modified Fermi-Hubbard model

How do I use this algorithm? What does that parameter do?
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pasa
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Joined: 09 Mar 2020, 12:45

Modified Fermi-Hubbard model

Post by pasa »

Dear Tenpy community,

happy new year all! I would like to ask you: How would you use TEBD for a MultiCouplingModel? The thing is that I need to add a longer-range coupling to my Hamiltonian and thus I cannot really use the Nearest neighbour model option.

I thought grouping sites but I am still missing something.
Thanks!
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Johannes
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Location: TU Munich

Re: Modified Fermi-Hubbard model

Post by Johannes »

If you have at most next-nearest neighbor interactions in a 1D chain, you can group sites and then perform TEBD.
In general, I'd recommend to switch to another time evolution algorithm, though:
either TDVP or the tenpy.algorithms.mpo_evolution.ExpMPOEvolution can deal with longer range.
The latter even has the same call structure as TEBD ;-)
pasa
Posts: 23
Joined: 09 Mar 2020, 12:45

Re: Modified Fermi-Hubbard model

Post by pasa »

Hi Johannes,

thanks for the advise! So my first thought was grouping sites to use TEBD and then Umberto kindly explained to me that apart from that, I had to convert my coupling model to a nearest neighbor model to use TEBD (actually he pointed out a really nice example code). So that works! But I also thought about using TDVP as it looks to be more natural. So, I wanted to ask you: What is the reason for your recommendation? What are the disadvantages of grouping sites wrt using TDVP? (At the end I will have to use TEBD grouping sites as I want to avoid using too many different numerical approaches.)

Thanks!
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Johannes
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Location: TU Munich

Re: Modified Fermi-Hubbard model

Post by Johannes »

Well, TEBD is nice because it is conceptually very simple - you just use a Suzuki-Trotter decomposition and straight forward iterations of (apply two site gate; compress & split to get back to MPS form). Grouping sites makes things more costly, however - formally TEBD scales as \(\mathcal{O}(\chi^3 d^3)\), so if you take d=2 -> d=4 by grouping sites, everything will be roughly 8 times as expensive!

TDVP and the MPO evolution, on the other hand, are built with long-range interactions in mind - they are designed for it, and don't suffer from such an increase of cost with longer range interactions.
For more arguments, see arXiv:1901.05824
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