Nematic Quantum Criticality in Dirac Systems

TL;DR

This paper studies nematic quantum phase transitions in Dirac systems using quantum Monte Carlo and renormalization group methods, revealing continuous transitions with large velocity anisotropies and crossover behavior.

Contribution

It provides the first combined numerical and analytical analysis of nematic quantum criticality in Dirac systems, highlighting slow approach to fixed points and crossover effects.

Findings

Both models exhibit continuous phase transitions.

Large velocity anisotropies characterize the quantum critical regime.

Crossover effects dominate the approach to the infrared fixed point.

Abstract

We investigate nematic quantum phase transitions in two different Dirac fermion models. The models feature twofold and fourfold, respectively, lattice rotational symmetries that are spontaneously broken in the ordered phase. Using negative-sign-free quantum Monte Carlo simulations and an $\epsilon$-expansion renormalization group analysis, we show that both models exhibit continuous phase transitions. In contrast to generic Gross-Neveu dynamical mass generation, the quantum critical regime is characterized by large velocity anisotropies, with fixed-point values being approached very slowly. Hence both experimental and numerical investigations will not be representative of the infrared fixed point, but of a crossover regime characterized by drifting exponents.