Chiral symmetry breaking and competing orders in correlated quantum matter and materials

• Applicant: Dr. Friederike Ihssen
• Subject Area: Theoretical Condensed Matter Physics ; Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 574031240

Recent experiments have measured a relativistic Mott transition in twisted double bilayer tungsten diselenide, a moiré material. The setup of this experiment (and similar ones) allows controlled access to quantum phase transitions in a bench-top setting. In my project, I want to develop a quantitative theoretical description of these phase transition phenomena by drawing on parallels and methods from particle physics and in particular quantum chromodynamics (QCD). The latter is known for its rich phase structure, emergent composite particles, superconducting states and inhomogeneous phases and was the topic of my PhD research. The project is structured in three parts: First, I will use non-perturbative functional renormalisation group (RG) methods to investigate which types of order are quantitatively relevant in a given moiré material in project (A). Secondly, I will use the RG in combination with advanced methods from numerical fluid-dynamics, Discontinuous Galerkin methods, to compute the free energy with a fully field dependent order parameter potential in project (B). The RG with full order parameter potentials is able to resolve if a phase transition is of first- or second order, and can detect which competing type of order dominates the phase structure if multiple order parameter fields are considered. Lastly, in project (C) I will further develop the formalism to extract response functions from the numerical data obtained in (B) and confront the results with experiment. In combination, projects (A)-(C) aim at a quantitative description of spontaneous symmetry breaking in strongly-correlated and strongly coupled condensed matter systems.

• DFG Programme: WBP Position