Fermion-induced quantum critical points in three-dimensional Weyl semimetals

TL;DR

This paper explores fermion-induced quantum critical points in three-dimensional Weyl semimetals, demonstrating a continuous transition with emergent symmetry at a putatively first-order $Z_3$ transition, supported by lattice models and renormalization-group analysis.

Contribution

It introduces the concept of FIQCPs in 3D Weyl semimetals, showing that $Z_3$ symmetry-breaking transitions can be continuous due to fermion fluctuations, with implications for experimental detection.

Findings

Identification of a $Z_3$ nodal-nematic transition in 3D double-Weyl fermions.

Renormalization-group analysis shows cubic terms are irrelevant at the transition.

Emergence of U(1) symmetry at low energy indicates a genuine FIQCP.

Abstract

Fermion-induced quantum critical points (FIQCPs) were recently discovered at the putatively first-order transitions between two-dimensional (2D) Dirac semimetals and the Kekule valence bond solids on the honeycomb lattice by sign-free quantum Monte Carlo simulations [Nature Communications 8, 314, (2017)]. Here, we investigate possible FIQCP in 3D topological Weyl semimetals at a $Z_3$ symmetry-breaking transition that is putatively first-order according to the Landau criterion. We construct a lattice model featuring 3D double-Weyl fermions (monopole charges $\pm$2) and we show that $Z_3$ nodal-nematic transitions occur under finite Hubbard interaction. Furthermore, using renormalization-group analysis, we identify such a transition as a genuine FIQCP where the cubic terms are irrelevant and an enlarged U(1) symmetry emerges at low energy. We further discuss quantum critical behaviors and experimental signatures of such FIQCPs in 3D double-Weyl semimetals.