TeNPy Forum

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!

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

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!

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