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TT: Fachverband Tiefe Temperaturen

TT 22: Focus Session: Frustrated Magnetism and Local Order (joint session MA/TT)

TT 22.2: Invited Talk

Tuesday, March 19, 2024, 10:00–10:30, H 1058

Frustrations, glassiness and complexity of spin systems with large spatial dimension — •Mikhail Katsnelson — Radboud University, Nijmegen, Netherlands

It was suggested some time ago [1] that spin system can behave as a glass without disorder, due to frustrations only (self-induced spin-glass state). Recent experimental discovery of glass-like magnetic state in elemental Nd at low temperatures [2] creates a very strong motivation to improve our theoretical understanding of such an opportunity. We have shown [3] that the glassiness without disorder can be derived quite rigorously for classical Heisenberg model in the limit of large spatial dimension, where an accurate and controllable mathematical treatment turns out to be possible.

For frustrated quantum spin systems, the sign structure of the ground state has a high complexity, in a sense that the machine learning of this structure is very difficult [4]. This problem however can be mapped to the classical Ising model of a very large dimension which allows to reach a progress in determining this sign structure [5].

[1]. A. Principi and M. I. Katsnelson, Phys. Rev. B 93, 054410 (2016); Phys. Rev. Lett. 117, 137201 (2016). [2] U. Kamber et al, Science 368, eaay6757 (2020); B. Verlhac et al, Nature Phys. 18, 905 (2022). [3] A. Mauri and M. I. Katsnelson, arXiv:2311.09124. [4] T. Westerhout et al, Nature Commun. 11, 1593 (2020). [5] T. Westerhout, M. I. Katsnelson, and A. A. Bagrov, Commun. Phys. 6, 275 (2023).

Keywords: frustration; self-induced spin glass; ground state wave function; machine learning; limit of infinite dimensionality