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Quantum geometry and topology with (a) spin

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If you have a question about this talk, please contact Bo Peng .

The geometry of quantum states has long attracted attention in various communities, as it is useful in optics, superfluidity and perhaps most intriguingly quantum metrology. Recently, it has been shown that the topology of a set of quantum states constrain their geometry in a non-trivial way.

In this talk, I will begin by defining quantum geometry, and its relation to Chern topology in time-reversal symmetry broken systems. I will then discuss how to extend these ideas to time-reversal symmetric systems, by considering the projected spin spectrum.

The latter part of the talk will be largely based on: W. J. Jankowski, R.-J. Slager, and G. F. Lange, Quantum geometric bounds in spinful systems with trivial band topology (2025), arXiv:2501.16428.

This talk is part of the Theory of Condensed Matter series.

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