Quantum Critical Matter: From Frustrated Spins to Interacting Fermions and Emergent Gauge Fields

• Applicant: Dr. Lukas Janssen
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 411750675

Many phenomena in condensed matter can be rationalized in terms of weakly-interacting quasiparticles. However, in strongly-correlated materials, the dominance of electronic interactions can give rise to novel collective behavior, which cannot be understood within effective one-particle descriptions. Such a situation arises in particular in the vicinity of a continuous zero-temperature phase transition point, dubbed quantum critical point (QCP). Near a QCP, new types of excitations emerge: They may be quasiparticle excitations with fractionalized quantum numbers interacting with an emergent gauge field, or they may not admit a quasiparticle description at all. Both cases lead to fascinating phenomena that are only poorly understood to date. QCPs, although being isolated points in a system's phase diagram, leave their imprints on observables even significantly away from the actual transition and hence provide ideal starting points to reveal the intriguing physics of quantum materials. The project aims at a thorough understanding of a variety of strongly-correlated systems from the common viewpoint of quantum criticality. This will include models for frustrated magnets and interacting semimetals in different dimensions, as well as quantum critical systems that are described by emergent gauge field theories. What are the characteristic excitations? What are the relevant interactions? What is the nature of the QCP and its adjacent phases? How can a material be tuned through a QCP into a regime that stabilizes a novel quantum phase? Answering these questions will allow us to gain unprecedented insight into the intricate nature of strongly-correlated quantum matter, and might eventually even lead to novel applications. We will employ and further develop suitable many-body tools, such as mean-field techniques, 1/N and epsilon expansions, the functional renormalization group, and nonperturbative field-theoretical dualities. The project is designed to benefit from recent symbiotic developments in condensed-matter, high-energy, and statistical physics, and is intended to also further advance these emergent bridges between different subfields of physics.

• DFG Programme: Independent Junior Research Groups