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I want to learn tensor network methods for condensed matter systems. I went through some basic papers (i.e. 1,2) and come to know that there are many things (i.e. different math, tensors, renormalization groups, entanglement) that I do not know. My current goal is to find the ground state energy and wavefunction of simple 1D spinless chain using tensor networks methods (i.e. matrix product states).

I would really appreciate if someone please provide me a proper roadmap by which I can learn this technique in a systematic way. A map from the basic theory to the coding of tensor networks.

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  • $\begingroup$ I've deleted some comments, and would remind everyone that comments are for suggesting improvements to, or requesting clarifications on, the parent post - not for answering. $\endgroup$
    – David Z
    Dec 30, 2018 at 0:55
  • $\begingroup$ @DavidZ You seem to have removed the book suggestion which OP had found very useful. $\endgroup$
    – Sunyam
    Dec 30, 2018 at 14:06
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    $\begingroup$ @Sunyam Yes, that's correct. Answers to the question should not be posted as comments. $\endgroup$
    – David Z
    Dec 30, 2018 at 20:47
  • $\begingroup$ I think it is better to first have the answer and than erase the comment, and not the other way around. $\endgroup$
    – proton
    Jun 18, 2019 at 16:27

2 Answers 2

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The references you provided are already very solid. For a summary of modern approaches I recommend additional the review Time-Evolution methods for matrix-product states. Regarding the coding there are countless libraries. Depending on your coding skills (basically the question is C++ or Python) you can take a look into ITensor or TenPy for example. But anyway as a general starting point for tensor networks I would recommend to learn how to perform tensor contractions (e.g. with tensordot) and a singular-value decomposition (e.g. with svd). Starting codes for tensor network algorithms like TEBD or DMRG can further be found on mpipks.

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The following website provides excellent resources for tensor networks which are curated for different goals such as Fundamentals, Types of Tensor Networks, Tensor Network Algorithms, Software, Application to different areas.

https://tensornetwork.org/

As suggested in the previous answer ITensor or TenPy is a good way to start with hands-on learning which is my preferred way of learning.

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