Many-Body Localization and Complex Networks: new challenges for quantum ergodicty – ManyBodyNet

One of the major frontiers of modern physics concerns the emergence of unconventional quantum regimes governed by disorder and interactions. Despite significant progress in recent years, a number of phenomena are still very poorly understood, such as the so-called many-body localization (MBL), which is deeply related to the non-ergodic and glassy nature of certain disordered quantum systems. New theoretical efforts are therefore needed in a highly competitive international context where many important experimental developments are also underway. These efforts necessarily require a strengthening of our modeling tools, such as simplified random matrix models, numerical simulations, as well as advanced analytical developments, all of which are crucial to unlocking a deeper understanding of the exciting new phenomena emerging in this field. In addition, it is essential to maintain close contact between theoretical models, fundamental questions, and the various experimental platforms available today, so that a fruitful cross-fertilization takes place.

To meet this ambitious challenge, we have set up this new collaboration consisting of 4 nodes where unique and perfectly complementary skills will be synergized: high-performance numerical simulations; theory of disordered systems, graphs and random matrices; glassy systems. This project tackles the fundamental challenge of quantum non-ergodicity in two key, interconnected settings: complex geometries and many-body interactions. This should allow us to make progress and deepen our understanding of the MBL problem, in particular through the investigation of the deep links that exist between 3 fundamental research areas: many-body localization (MBL), complex networks, and random matrix theory. Our theoretical proposal, however, will maintain a strong connection with experimental platforms. Since this interplay fuels both theory and experiment, we plan to boost the exploration of this dimension in several directions. Indeed, very recent productive discussions with two experimental groups have yielded valuable insights and shaped our research direction. In particular we propose further concrete exchanges with two experimental teams:The I. Bloch's Quantum Optics Group at LMU, who plans to leverage their new Cs experiment to precisely control interaction strength using Feshbach resonances; this setup offers a perfect platform to validate a recently proposed theoretical scenario by our team. The Q. Ficheux's Superconducting Quantum Circuits group at Institut Néel, who is constructing an artificial spin chain with tunable couplings based on fluxonium circuits. This innovative system will provide key tests for fundamental questions arising from quantum disordered Ising chain models.

Our ManyBodyNet project is unique in that, probably for the first time, it brings together highly complementary and cutting-edge expertise in several fields related to localization, interactions and glassy systems. We also believe that the establishment of this collaboration is a major asset in meeting the many challenges posed by this highly competitive field of condensed matter at international level.