Visn. Nac. Akad. Nauk Ukr. 2016. (12):63-73
https://doi.org/10.15407/visn2016.12.063

I.V. Krive, S.I. Shevchenko
Verkin Institute for Low Temperature Physics and Engineering of the National Academy of Sciences of Ukraine, Kharkiv

NEW PHASES OF QUANTUM MATTER AND TOPOLOGY
Nobel Prize in Physics for 2016

In 2016 the Nobel Committee in Physics awarded Prof. D.J. Thouless (1/2 prize), Prof. J.M. Kosterlitz (1/4 prize) and Prof. F.D.M. Haldane (1/4 prize) for “theoretical discovery of topological phase transitions and topological phases of matter”. We discuss new ideas and the results of papers where (i) topological phase transitions (Berezinskii–Kosterlitz–Thouless phase transitions) in two-dimensional condensed matter were theoretically predicted, (ii) a deep connection between quantization of the Hall conductivity in 2D systems with violated T-invariance and topological quantities (Chern invariant) was revealed (Thouless–Kohmoto–Nightingale–den Nijs), (iii) new quantum phase (Haldane phase) of spin chains with integer spin was predicted. Main attention was given to qualitative explanation of the predicted new phenomena. We follow the interconnections between the cited works of Nobel laureates and low-dimensional models of relativistic quantum field theory where the crucial role of topological invariants in the special phases of quantum matter was first noted.

Keywords: topological phase transitions, topological phases, topological invariants, Hall conductivity, spin chains.

Language of article: ukrainian

 

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