Probing super-ballistic information propagation in long-range quantum spin systems

• Applicant: Professor Marius Lemm, Ph.D.
• Subject Area: Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas ; Mathematics ; Theoretical Condensed Matter Physics
• Term: since 2026
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 465199066

A central problem in non-equilibrium quantum physics is to understand the speed of information propagation in interacting many-body systems. The celebrated Lieb-Robinson bound limits the propagation speed for short-ranged interactions and has led to numerous influential applications in condensed-matter physics and quantum information science. Over the past decade, the mathematical methods underlying the Lieb-Robinson bound have been extended to quantum systems with long-ranged interactions. Recent results prove that the speed of information propagation remains controlled if the power-law exponent of the interactions is less than twice the spatial dimension plus one. Below this threshold, the bounds permit super-ballistic information propagation. The key point is that in many cases the physically relevant long-range interactions that are native to common experimental platforms (e.g. Rydberg tweezer arrays) are more long-ranged than the threshold and so these existing theoretical propagation bounds in principle allow for super-ballistic information propagation. Concrete examples that this applies to are dipolar interactions in 2D and van der Waals interactions in 3D. The physical implications of super-ballistic transport are multi-faceted and depend on the task at hand: While it makes the system dynamics less controllable, it enables extremely rapid state and entanglement transfer that could substantially speed up information-theoretic protocols. The objective of this project is to systematically investigate the extent to which super-ballistic information propagation is indeed realized for the types of long-range interactions relevant in Rydberg systems. We pursue a novel holistic approach that bridges from mathematical to experimental physics. One focus is to derive enhanced Lieb-Robinson bounds which establish that transport is at most ballistic for a wider range of power law exponents by exploiting physically relevant structural features of the Hamiltonians (e.g., time-independent interactions or disorder) that have not been used before. For this, we rely on the mathematical expertise of the two PIs in the analytical techniques underpinning Lieb-Robinson bounds for long-range interacting systems. Another focus is to devise an experimental scenario to enable the first observation of super-ballistic propagation in a 2D quantum system. For this purpose, we collaborate with the group of C. Gross which is working on realizing the 2D XY model with a Rydberg tweezer array. This project thus aims to exploit the full breadth of the Tübingen quantum physics ecosystem to address a fundamental and urgent problem in non-equilibrium quantum physics - probing super-ballistic information propagation in long-range interacting quantum spin systems.

• DFG Programme: Research Units
• Subproject of: FOR 5413: Long-range interacting Quantum Spin systems out of equilibrium: Experiment, Theory and Mathematics
• Co-Investigator: Professor Dr. Stefan Teufel