andras_mail.md (2054B)
1 Dear Milutin, 2 3 Thanks for the interest. Please find below some references. I'm also 4 happy to talk next week, feel free to drop by (I'm in the office in 5 front of ESI, write me an email before coming). 6 7 This <https://arxiv.org/abs/2011.12127> is a general review about 8 tensor networks (just in case). Maybe a good place to start to learn 9 about PEPS and the context in which it is used.In this paper 10 <https://arxiv.org/abs/1804.04964> we show how symmetries are reflected 11 in PEPS that describes systems without any topological order. This 12 paper is just a proof, and it is quite technical, so it won't help you 13 to understand the general concepts. If you like proofs though it might 14 be interesting. 15 Symmetries in PEPS are strongly linked to topological order. The 16 introduction part of these lecture notes 17 <https://arxiv.org/abs/1506.05805> might be useful to understand the 18 different kind of topological orders one might encounter. That being 19 said, 20 This paper <https://arxiv.org/abs/1106.4752> is the first example how 21 to describe symmetry protected topological (SPT) order in PEPS.This 22 paper <https://arxiv.org/abs/1001.3807> shows how PEPS can describe 23 systems with topological order, for the simplest type of intrinsic 24 topological order. If you are not afraid to dive into category theory, 25 this paper <https://arxiv.org/abs/1410.4540> provides a classification 26 of topological phases with symmetry (symmetry enriched topological 27 phases, SET). This is not about PEPS, but the ideas behind are the same 28 anyway. In this paper <https://arxiv.org/abs/1711.07982> examples for 29 the above SET classification have been constructed using PEPS. 30 I think the last two papers are too hard/extensive for a seminar, but 31 it is nice to see where the theory can lead you. If you are interested 32 in topological order, then the G-injective paper 33 <https://arxiv.org/abs/1001.3807> might be the best to read from the 34 list above. As mentioned above, I am also happy to talk, maybe with a 35 personal meeting we can narrow down more what you actually are 36 interested in. 37 38 Best, 39 Andras 40