Quantum phase transitions in metallic systems pose a variety of challenges to theory: The simultaneous presence of low-energy electron-hole pairs and order parameter fluctuations can invalidate the standard order-parameter based Landau-Ginzburg-Wilson (LGW) description of the critical fluctuations. The objective of this project is a better understanding of the physics in the vicinity of such non-LGW quantum phase transitions.

First, we want to study the competition of low-energy phenomena in heavy-fermion metals in situations where the Fermi liquid coherence temperature is comparable to or smaller than other scales such as the Neel temperature, the superconducting transition temperature, or the Debye temperature.

Second, we plan to investigate in detail routes to non-LGW transitions, namely due to either the complete breakdown of the Fermi surface (perhaps realized in certain heavy-fermion metals), or the presence of multiple dynamic scales, specifically near Landau- Pomeranchuk instabilities with distinct order parameter modes.

A central question for the theory of quantum-critical points in heavy-fermion systems, both experimentally and theoretically, is the stability of the Fermi surface at the QCP. In a Kondo lattice model, the quenching of the local moments by the Kondo effect leads to the formation of a Fermi liquid (FL) with a "large" Fermi volume (counting both localized and itinerant electrons). Alternatively, the local moments can also be quenched by inter-moment interactions (e.g. of RKKY type) - this can result in a state with magnetic long-range order or in a spin liquid without any broken symmetry.

Proposed phase diagram for a quantum critical point in heavy-fermion metals. The primary transition is from FL to FL* where the Kondo effect breaks down, whereas magnetism is a secondary instability of FL*

In the latter case, a paramagnetic phase emerges, with a "small" Fermi surface that encloses only the conduction electrons but not the localized spins. As the excitations in such a spin liquid are fractionalized while the conduction electrons can be described by Fermi liquid theory, we dubbed this phase a "fractionalized Fermi liquid" FL*. While this state may be unstable towards magnetism at lowest energies, the quantum phase transition from FL to FL*, associated with the breakdown of the Kondo effect, controls the non-Fermi liquid quantum critical regime of the phase diagram.

Clearly, the Kondo-breakdown transition is not of conventional Landau-Ginzburg-Wilson type. It is characterized by the re-organization of the Fermi surface and a jump in the Fermi volume. Within this project, transport properties near this transition shall be studied in more detail.

Numerous quantum phase transitions are characterized by the presence of multiple diverging time scales, corresponding to different dynamic exponents. Then, standard scaling concepts and renormalization approaches need to be modified.

We want to investigate this situation for the simple example of Landau- Pomeranchuk instabilities of two-dimensional isotropic Fermi liquids. Here, the structure of the order parameter leads to two types of modes with distinct Landau damping, corresponding to two distinct dynamic exponents. Both physical and methodological consequences will be explored.