0 votes
asked by (130 points)

Hi, I am trying to evaluate the infinite temperature expectation value of an operator at different times in a spin-1 chain, as in Fig. 1 of https://arxiv.org/abs/1904.04266.
The Hamiltonian contains three sites terms (Eq. 1 in the article), so I cannot use toExp() for the time evolution. Any idea of how I could overcome this problem?

I tried using the TDVP library but it time-evolves the MPS, it seems I need to use Heisenberg representation to time-evolve the MPO.


1 Answer

0 votes
answered by (14.1k points)

The easiest way I could think of would be to use the TEBD algorithm, which would be easy enough in the C++ or Julia versions. Have you looked into that?

You can look here:


and here:


commented by (130 points)
Hi, thank you for the quick answer.
I have watched the method used in the link for C++, but it relies on the BondGate class which only works for two-site gates, so I don't think it is of help for my case.

Do you have any other tip?
commented by (14.1k points)
The easiest thing to do if you are using the C++ library would be to make a new BondGate class, for example called BondGate3, by copying and modifying the current BondGate class to allow for 3-site gates (essentially by adding a third data field `i3` and modifying the constructors of the class to accept that 3rd position). Then you would need to write a modified version of the gateTEvol function (https://github.com/ITensor/ITensor/blob/684bb4207da536dce59f1f2589b60ec23d1d61cb/itensor/mps/tevol.h ) which worked with the `BondGate3` gates.

Otherwise, in the Julia version, you can already directly make 3-site gates and they will work with the `apply` function, by generalizing the example http://itensor.org/docs.cgi?vers=julia&page=getting_started/mps_time_evolution .
commented by (130 points)
Thank you very much, I will try what you suggested for c++.
Welcome to ITensor Support Q&A, where you can ask questions and receive answers from other members of the community.

Formatting Tips:
  • To format code, indent by four spaces
  • To format inline LaTeX, surround it by @@ on both sides
  • To format LaTeX on its own line, surround it by $$ above and below
  • For LaTeX, it may be necessary to backslash-escape underscore characters to obtain proper formatting. So for example writing \sum\_i to represent a sum over i.
If you cannot register due to firewall issues (e.g. you cannot see the capcha box) please email Miles Stoudenmire to ask for an account.

To report ITensor bugs, please use the issue tracker.