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I am trying to implement the iTEBD algorithm for the $PXP$ model, i.e, the hamiltonian is

$$H = \sum_iP_{i-1}X_iP_{i+1}.$$

Here $P$ is the projector onto the ground state and $X$ is the usual pauli x matrix.

I aim to time evolve a certain initial state and record certain observables. To do so, I initialized my iMPS (infinite Matrix Product State), and as a check, I took the overlap of this with itself. As I expected, this gave me a result of 1. However, it appears that as I time evolve my state, the normalization strays further from unity, and by the last time step, it is of the order 1e5. I know that we perform a truncation in each time step, but my question is can this introduce such a large error?

I have used a trotter step of 0.01, and a bond dimension of 50, and I have evolved for 20-time steps. For context, I am trying to time-evolve a state that resembles the Neel state, i.e it looks like $|...0101...\rangle$

Edit: it appears that the norm squared is jumping around rather than just increasing Plot of norm over time

The link to my code is below for anyone who is interested

https://colab.research.google.com/drive/12p8c6UJB5M49tOJqbTno1bZpUfc_I-mB?usp=sharing

As this is the first time I am working with tensor networks and I haven’t seen any examples online of 3-body hamiltonians, I would also like to get it cleared if there would be any particular differences in applying 3-body vs 2-body hamiltonians. Right now what I do is contract 3 site tensors, apply the time evolution operator, and SVD out the resulting tensor.

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    $\begingroup$ Consider to spell out acronyms. $\endgroup$
    – Qmechanic ♦
    Commented Dec 26, 2022 at 8:20
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    $\begingroup$ Would Computational Science be a better home for this question? $\endgroup$
    – Qmechanic ♦
    Commented Dec 26, 2022 at 8:21
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    $\begingroup$ I’m voting to close this question because this belongs to the Computational Science site. $\endgroup$
    – Miyase
    Commented Dec 26, 2022 at 9:09
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    $\begingroup$ @Miyase How much do you know about the topic of the question? This is about a simulation method used for time evolution of quantum many-body systems, and thus rather specific to physics. Conversely, I would be interested to see at least one question at Comp. Science answering a question in that direction -- I couldn't find one with a quick search. On the other hand, I know that here, there are at least a few people who could answer this. $\endgroup$
    – Norbert Schuch
    Commented Dec 26, 2022 at 9:37
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    $\begingroup$ @Souroy If you have an error, it will accumulate - so to decrease the error you need smaller Trotter steps. But I would think the norm in iTEBD, done the usual way, should get smaller by truncation, not larger. -- I'd suggest doing sanity checks to see if you have a bug. $\endgroup$
    – Norbert Schuch
    Commented Dec 26, 2022 at 9:43

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