Topological Properties of Exceptional Points


Tuesday, November 14, 2023
10:30 - 11:30


Recent years have marked a paradigm shift within physics research as systems effectively described by non-Hermitian Hamiltonians have gained vastly increased attention [1]. Prominent distinction from their Hermitian counterpart includes a modified bulk-boundary correspondence and the generic appearance of exceptional points, where both eigenvalues and eigenvectors coalesce. At these points, the eigenbasis of the Hamiltonian does not span the Hilbert space, which leaves the Hamiltonian defective and hence non-diagonalizable.

In this talk, I will give a brief survey of recent years progress within the studies of exceptional points in generic non-Hermitian systems [2,3] and such subject to parity-time symmetry [4-8]. I will focus on the connection to various mathematical venues, including algebraic topology, knot theory and complex dynamics to mention a few examples, but also provide a broader perspective and discuss the experimental relevance of these systems. I will also point towards what, according to me, are interesting future directions, which includes connections to quantum information and realizations in fully quantum setups.

My goal is, despite the apparent abstractness, to provide an overview talk emphasizing conceptual understanding and thus including as few calculation details as possible. In this way, I hope that the talk will be accessible to those who are previously unfamiliar with the topic.

[1] E.J. Bergholtz et. al., Rev.Mod.Phys. 93, 15005 (2021).
[2] J. Carlström et. al., Phys.Rev.B 99, 161115 (2019).
[3] M. Stålhammar et. al., SciPostPhys. 7, 019 2019.
[4] M. Stålhammar et. al., Phys.Rev.B 104, L201104 (2021).
[5] M. Stålhammar et. al., New. J. Phys. 25, 043012 (2023).
[6] S. Sayyad et. al., arXiv:2204.13945 (Accepted in SciPost Physics).
[7] M. Stålhammar et. al., Phys. Rev. Research 5, 043043 (2023).
[8] K. Yang et. al., arXiv:2309.14416


Soft Matter group


UvA - Faculty of Science

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computational physics, condensed matter theory, hard condensed matter, soft matter


Marcus Bäcklund

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