Interacting spin waves in quantum antiferromagnets in two dimensions.

• Applicants: Professor Dr. Kai Phillip Schmidt; Professor Dr. Götz S. Uhrig
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 434439878

This project builds on the recent methodological progress fornon-perturbative continuous similarity transformations (CSTs) in momentum space,which enables a quantitative understanding of the magnetic excitations and their dynamic correlations of the paradigmatic square-lattice Heisenberg model. The CST maps the strongly correlated quantum many-body problem to an effective model conserving the number of dressed spin waves with strong mutual attractive interactions. Here we extend this approach in two directions: First, we consider unfrustrated deformations of the square-lattice Heisenberg model such as the easy-axis XXZ model, the bilayer square-lattice Heisenberg model, and the so-called J-Q-model, so that the quantum-critical breakdown of the long-range Neel order can be investigated via the spectral properties of dressed spin waves and of the Higgs amplitude modes. Second, we add geometric frustration to the square-lattice Heisenberg model. Specifically, we focus on the J1-J2-model on the square lattice and on the spatially anisotropic triangular lattice. In both cases, the decay of spin waves in large parts of the Brillioun zone and the formation of bound states state is expectedin the magnetically ordered phases. The description of these phenomena requiresmodifications of the CST scheme which is developed in this project and which allows us to gain novel insight into the quantum phase transitions fromthe magnetically ordered state to the potential quantum spin liquids in these frustrated quantum magnets.

• DFG Programme: Research Grants