Symmetric tensor networks for 2d quantum matter

• Applicant: Professor Dr. Matteo Rizzi, since 9/2018
• Subject Area: Theoretical Condensed Matter Physics ; Optics, Quantum Optics and Physics of Atoms, Molecules and Plasmas
• Term: from 2017 to 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 358346317

In spite of the progress in the theory of 2d quantum systems, a full understanding of them is still missing. Within this setting, this project will develop new methods to solve long-standing open problems in 2d condensed matter physics which are key in our understanding of quantum matter, such as the physics of frustrated quantum magnets, and chiral topological quantum spin liquids. For this, we will study, both analytically and numerically, the properties of 2d quantum many-body systems with non-abelian symmetries using Projected Entangled Pair States (PEPS), which are Tensor Network (TN) representations of quantum states. In particular, we will exploit new classification schemes of 2d SU(2) quantum spin liquids to search for new chiral topological bosonic and fermionic PEPS, and will also develop new general-purpose numerical methods for 2d systems with non-abelian symmetries. Introducing non-abelian symmetries in the game is a challenge, and will bring unprecedented accuracy to calculations of, e.g., low-energy properties. On top of the mid-term impact in the study of 2d quantum matter, this project will also be the basis for a new era in TN methods in the long term. The produced numerical toolbox will have an impact in wide spectrum of fields such as condensed matter physics, quantum-atom optics, lattice gauge theory, quantum information, quantum chemistry, and computational physics.We intend to start with the project directly; the planned duration is three years.

• DFG Programme: Research Grants
• International Connection: France
• Cooperation Partners: Dr. Matthieu Mambrini; Professor Dr. Didier Poilblanc; Professor Hong-Hao Tu, Ph.D.
• Ehemaliger Antragsteller: Professor Dr. Roman Orus, until 8/2018