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Séminaire MCBT : lundi 6 novembre 2023 à 14h00


Jeanne Colbois (Laboratoire de Physique Théorique, Université de Toulouse, CNRS)


Titre : Introduction to tensor networks for classical frustrated spin systems


Institut Néel, Salle E424 (Salle Louis Weil)
Résumé : Despite their apparent simplicity, classical antiferromagnetic Ising models on frustrated lattices give rise to exotic phases of matter, in particular due to their macroscopic ground-state degeneracy. They also represent an interesting numerical challenge for classical Monte Carlo approaches, requiring the design of ad hoc cluster updates. Motivated by problems stemming from artificial spin systems [1], I will describe a framework to study frustrated models with nearest-neighbor and farther-neighbor interactions directly in the thermodynamic limit using infinite tensor networks [2, 3]. I will start by introducing the tensor network language and associated algorithms from the transfer matrix perspective, before discussing the specific challenges encountered when studying frustrated models, and some ways to work around them. The power of these methods will be illustrated through applications to frustrated models on the triangular and kagome lattices [4, 5].
1) I. A. Chioar, N. Rougemaille, and B. Canals, Phys. Rev. B 93, 214410 (2016).
2) B. Vanhecke, J. Colbois, et al., Phys. Rev. Research 3, 013041 (2021).
3) F.-F. Song, T.-Y. Lin, and G.-M. Zhang, Arxiv:2309.05321, (2023).
4) J. Colbois, B. Vanhecke, et al., Phys. Rev. B 106, 174403 (2022).
5) S. Nyckees, A. Rufino, F. Mila, and J. Colbois, Arxiv:2306.09046, (2023).