MajuLab Seminar by Olivier Giraud – 11 April 2024

Olivier Giraud is senior researcher (Directeur de recherche) at CNRS. He obtained his PhD on quantum chaos at Université Paris Sud. After a post-doctoral stay at the University of Bristol, he spent 5 years at Laboratoire de Physique théorique in Toulouse, where he worked on theoretical aspects quantum information. In 2010 he joined Université Paris Saclay, working on metrology and complex networks. Since 2023 he is working at MajuLab and a visiting research associate professor at CQT. His fields of interest include random matrices, quantum entanglement, complex networks.

Seminar

Probing symmetries of quantum many-body systems through ratio statistics

The idea of describing properties of complicated systems, such as complex atomic nuclei, by random matrices dates back to the 1950s. It provides a tool for understanding the statistics of discrete energy levels. In particular, the statistical distribution of the spacings between successive energy levels gives a signature of whether the system behaves in a regular or a chaotic way. Random matrix theory has found applications in many branches of physics but also in biology or finance.

For practical reasons, the focus has shifted in recent years from the statistics of energy spacings to the statistics of ratios between successive spacings. This ratio statistics is by now a widely used tool of quantum chaos, that allows to compare experimental or numerical observations with theoretical predictions. However, extra symmetries of the system, which may be hidden, can modify these statistics. We show that it is possible to extend the theory of spacing ratio statistics to account for the presence of additional symmetries. Our results allow to probe for the existence of symmetries if they were unknown. We derive analytical surmises for random matrices with independent block structure, and illustrate our approach on a number of applications from many-body physics. This provides a tool not only to get a signature of chaos or regularity in systems with symmetries, but also to uncover these symmetries if they were previously unnoticed.

MajuLab is an international joint research unit of the CNRS, UCA, SU, NUS and NTU in Singapore (IRL 3654), hosted by CQT and SPMS.