Symmetry-enforced topology in many-body physics

• Applicant: Dr. Moritz Hirschmann
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2023
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 518238332

If I am awarded with a Walter Benjamin fellowship to support my research position at RIKEN, Japan, I will, broadly speaking, investigate the implications of crystalline symmetries on the properties of condensed matter. A primary focus of this research proposal lies on topology, which refers to the examination of properties that are invariant under continuous modifications of the object of study. Topology is not only important as a mathematical concept but also applies to many parts of physics, including the classification and description of various different solids. Of special interest are systems with correlations between their constituents. Correlations complicate our physical understanding but also lead to novel and exotic properties. In my work I am going to research the aforementioned aspects of condensed matter physics. I aim to establish novel symmetry-based approaches to describe the topology of many-body systems and to predict their measurable implications. (i) My first goal is to answer open questions concerning the stability of quantum phases in the presence of interactions. To do so, I want to identify topological invariants for correlated systems, by using the global constraints imposed by non-symmorphic symmetries and Lieb-Schultz-Mattis type arguments. (ii) I will employ so-called spin-space groups to discover the symmetry-enforced topology in the presence of unconventional magnetism and determine the consequences for electronic and magnonic systems. Spin-space groups capture the physics beyond the realm of magnetic space groups, but can still be treated by the group theoretical methods, with which I am already familiar through my previous works. (iii) I plan to derive the constraints imposed by non-symmorphic symmetries on the many-body eigenstates, which I expect to yield new guiding principles for the identification of topological phase transitions. In particular, these symmetry constraints may give criteria for the gaplessness of a many-body wave function, i.e., statements on the absence of a gap in the energetic spectrum, which is important for the understanding of physical properties.

• DFG Programme: WBP Fellowship
• International Connection: Japan
• Host: Dr. Akira Furusaki