Tensor-Network Methods for Strongly-Correlated Quantum Matter – TNSTRONG

A conceptual understanding of strongly correlated electronic materials is the main challenge of modern Condensed Matter theory. To address the phase diagrams of high-Tc superconducting cuprates or strongly frustrated quantum magnets or the physics of (Abelian or non-Abelian) fractional quantum Hall states one needs a reliable treatment of simple paradigmatic microscopic models such as extended Hubbard or frustrated Heisenberg models. The time is ripe to expect rapid progress in the field. On one hand, new promising methods based on quantum entanglement concepts - so-called tensor network (TN) methods - have just started to be applied to Condensed Matter problems with unprecedented success. Such methods also provide for the first time the correct framework for understanding topological order (which goes beyond Landau paradigm) present in very important classes of materials such as quantum spin liquids and fractional quantum Hall states. On the other hand, developments in Atomic Physics of cold atom "quantum simulators" will provide direct confrontations to the theoretical approaches and complement Solid State Physics experiments. Our ambitious project aims to develop innovating cutting-edge TN methods on two parallel complementary fronts: first, by designing simple paradigmatic wave functions to provide a deep understanding of the major phases of correlated systems (Spin liquids, fractional quantum Hall states and topological insulators, etc...) and, secondly, by attacking directly the key low-dimensional microscopic models using novel efficient TN optimization tools. The word-class expertise in state-of-the-art numerical and analytical techniques of the two PI’s Didier Poilblanc (DP) and Nicolas Regnault (NR) together with (i) potentially strong interactions with some of the members of DP’s Strongly Correlated Electron group (LPT-Toulouse) like Matthieu Mambrini or NR’s close collaborators like Benoit Estienne at LPTHE (Paris), and (ii) thanks to existing collaborations with the most renowned experts in the field of TN will be the keys to carry on successfully this ambitious project and solve the paradigmatic microscopic models essential to the scientific community working on correlated materials.