The notion of a free particle is the backbone of entire physics. Free particle systems are easy to understand because they can studied via numerous theoretical techniques or simulated in a laboratory. Luckily, nature is “not just a sum” of free particles, as there are many remarkable phenomena where interactions between particles give rise to far more complex phenomena, such as quantum entanglement or exotic phases of matter (high-temperature superconductors, spin liquids and topological insulators). However, quantifying and understanding the interaction effects in quantum systems remains a challenge because describing such systems is exponentially hard due to the very rapid increase of their Hilbert spaces.
In this project, you will develop a new approach to quantify the effect of interactions in quantum systems based on our recent idea of “interaction distance”, DF. Interaction distance measures the distance of any quantum state from the “closest” state of any free-particle system. This new tool allows to identify the effective free-particle description of a given quantum system based on specific patterns in its entanglement. Because of this novel point of view, we have already discovered surprising examples of free descriptions for systems which are naively expected to be strongly interacting.
Simply put, interaction distance allows us to map out the landscape of all quantum states in terms of the complexity of interaction effects in them (see figure). Apart from fundamental importance in quantum information, condensed matter physics and high-energy physics, interaction distance also provides a physical link with the recent approaches based on machine learning to describe quantum systems . Therefore, the second strand of this project is to investigate how to improve and physically benchmark these machine-learning methods for quantum many-body systems using interaction distance.
The fundamental understanding of interaction effects will be applied to several concrete problems, in particular how to use interactions to suppress dynamics in quantum systems, thereby extending robustness of encoded quantum information. More specifically, you will investigate the possibility of extending topological quantum memories to arbitrary temperature due to the mechanism of “many-body localisation” , and explain the origin of intriguingly slow dynamical regimes that have been observed in a recent 51-atom quantum simulator at Harvard .
Note: the project requires computational background (e.g., Python/Matlab/Julia/C++...).
References  Optimal free models for many-body interacting theories, Christopher J. Turner, Konstantinos Meichanetzidis, Zlatko Papic, Jiannis K. Pachos, Nature Communications 8, 14926 (2017); arXiv:1607.02679.  Machine learning: New tool in the box, Nature Physics 13, 420–421, doi:10.1038/nphys4053.  Many body localization and thermalization in quantum statistical mechanics, Rahul Nandkishore and David A. Huse, arXiv:1404.0686.  Probing many-body dynamics on a 51-atom quantum simulator, H. Bernien et al, arXiv:1707.04344.