The 2016 Nobel Prize in Physics was awarded to pioneering work opening the field of topological phases of matter. This field has matured later on in the study of the fractional quantum Hall effect [1], which continues to deliver exciting physics, in the form of non-abelian excitations and the observation of neutral edge modes [2]. Inspired by the quantum Hall effect, the study of non-abelian particles [3] has branched into different topics, such as the study of topological phases emerging in (spin) lattice models [4,5] and recently topological insulators and superconductors [6]. During recent years, the field of topological phases has been boosted by the possible application to quantum computing [7]. Implementing topological quantum computation in realistic experimental systems [8] is one of the holy grails of the community.

 The newly discovered two-dimensional (2D) topological spin liquids [9,10], some being close analogs of the FQHE, some providing completely new classes of exciting materials, are all charaterized by long-range entanglement. This fundamental feature makes it necessary to adapt and further develop with theoretical guidance state-of-the-art numerical techniques (Quantum MonteCarlo, DMRG, etc...) or invent new algorithms/methods able to attack such problem. Among them, tensor networks have demonstrated to be very promising. Such rapidly-progressing numerical methods are also now being developped to go beyong ground-state physics e.g. to investigate thermodynamics of condensed matters systems [11,12] or non-equilibrium physics [13] to tackle Floquet systems [14] and quantum simulators realized with cold-atom systems [15,16]. Applications to 3D frustrated magnets (e.g. pyrochlores etc...) with exotic ground states are now being investigated as well. 

Reference

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[2] M. Banerjee, M. Heiblum, V. Umansky, D. Feldman, Y. Oreg, A. Stern, Nature, 559, 205-210 (2018)
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[4] Bauer, B., Cincio, L., Keller, B. et al. Chiral spin liquid and emergent anyons in a Kagome lattice Mott insulator. Nat Commun 5, 5137 (2014).
[5] Ji-Yao Chen, Sylvain Capponi, Alexander Wietek, Matthieu Mambrini, Norbert Schuch, and Didier Poilblanc, Phys. Rev. Lett. 125, 017201 (2020).
[6] Jason Alicea, (review article) Rep. Prog. Phys. 75, 076501 (2012).
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[9] W. Liu, S. Gong, Y. Li, D. Poilblanc, W. Chen, Z. Gu, Science Bulletin, 67, 1034-1041 (2022)
[10] Wen-Yuan Liu, Juraj Hasik, Shou-Shu Gong, Didier Poilblanc, Wei-Qiang Chen, Zheng-Cheng Gu, Phys. Rev. X, in press (2022); arXiv:2110.11138.
[11] O. Gauthé, F. Mila, Phys. Rev. Lett., 128, 227202 (2022)
[12] J. Jiménez, S. Crone, E. Fogh, M. Zayed, R. Lortz, E. Pomjakushina, K. Conder, A. Läuchli, L. Weber, S. Wessel, A. Honecker, B. Normand, C. Rüegg, P. Corboz, H. Rønnow, F. Mila, Nature, 592, 370-375 (2021)
[13] Tim Langen, Remi Geiger, and Jörg Schmiedmayer,
Annual Review of Condensed Matter Physics 2015 6:1, 201-217.
[14] Takashi Oka and Sota Kitamura
Annual Review of Condensed Matter Physics 2019 10:1, 387-408.
[15] J. Dalibard, F. Gerbier, G. Juzeliunas, and P. Ohberg, (review article) Rev. Mod. Phys. 83, 1523 (2011).
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