# Regensburg 2019 – wissenschaftliches Programm

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# TT: Fachverband Tiefe Temperaturen

## TT 60: Quantum-Critical Phenomena (joint session TT/DY)

### TT 60.6: Vortrag

### Donnerstag, 4. April 2019, 16:15–16:30, H23

**Quantum critical behaviour in 2D Fermi systems with quadratic band touching** — •Shouryya Ray, Matthias Vojta, and Lukas Janssen — Institut für Theoretische Physik, Technische Universität Dresden, 01062 Dresden, Germany

We consider two-dimensional Fermi systems with quadratic band touching and *C*_{3} symmetry, as realizable in Bernal-stacked honeycomb bilayers. Within a renormalization-group analysis, we demonstrate the existence of a quantum critical point at a finite value of the density-density interactions, separating a semimetallic disordered phase at weak coupling from a gapped ordered phase at strong coupling. The latter may be characterized by, for instance, antiferromagnetic, quantum anomalous Hall, or charge density wave order. In the semimetallic phase, each point of quadratic band touching splits into four Dirac cones as a consequence of the nontrivial interaction-induced self-energy correction, which we compute to the two-loop order. We show that the quantum critical point is in the (2+1)-dimensional Gross-Neveu universality class, characterized by emergent Lorentz invariance and a dynamic critical exponent *z*=1. At finite temperatures, *T*>0, we hence conjecture a crossover between *z*=2 at intermediate *T* and *z*=1 at low *T*, and construct the resulting nontrivial phase diagram as function of coupling strength and temperature.