Phase transition with trivial quantum criticality in anisotropic Weyl semimetal

TL;DR

This paper reveals a trivial quantum critical point in an anisotropic Weyl semimetal, where quantum fluctuations are irrelevant, leading to mean-field behavior, contrasting with typical nontrivial quantum critical systems.

Contribution

The study demonstrates that anisotropic Weyl semimetals exhibit trivial quantum criticality with vanishing anomalous dimensions, simplifying the understanding of their phase transition.

Findings

Anomalous dimension of Weyl fermions flows to zero rapidly

Quasiparticle residue remains nonzero at low energies

Mean-field theory accurately describes the transition

Abstract

When a metal undergoes continuous quantum phase transition, the correlation length diverges at the critical point and the quantum fluctuation of order parameter behaves as a gapless bosonic mode. Generically, the coupling of this boson to fermions induces a variety of unusual quantum critical phenomena, such as non-Fermi liquid behavior and various emergent symmetries. Here, we perform a renormalization group analysis of the semimetal-superconductor quantum criticality in a three-dimensional anisotropic Weyl semimetal. Surprisingly, distinct from previously studied quantum critical systems, the anomalous dimension of anisotropic Weyl fermions flows to zero very quickly with decreasing energy, and the quasiparticle residue takes a nonzero value. These results indicate that, the quantum fluctuation of superconducting order parameter is irrelevant at low energies, and a simple mean-field calculation suffices to capture the essential physics of the superconducting transition. We thus obtain a phase transition that exhibits trivial quantum criticality, which is unique comparing to other invariably nontrivial quantum critical systems. Our theoretical prediction can be experimentally verified by measuring the fermion spectral function and specific heat.