Random-mass disorder in the critical Gross-Neveu-Yukawa models

TL;DR

This paper investigates how quenched random-mass disorder influences quantum phase transitions in Dirac materials, revealing new critical points, bifurcations, and emergent scale invariance using advanced field-theoretic methods.

Contribution

It introduces a controlled epsilon expansion approach to analyze disordered Gross-Neveu-Yukawa models, uncovering novel critical phenomena and bifurcation scenarios.

Findings

Discovery of new finite-randomness critical points with nonzero Yukawa coupling.

Identification of bifurcation scenarios including fixed-point annihilation and Hopf bifurcation.

Observation of emergent discrete scale invariance at fermionic quantum criticality.

Abstract

An important yet largely unsolved problem in the statistical mechanics of disordered quantum systems is to understand how quenched disorder affects quantum phase transitions in systems of itinerant fermions. In the clean limit, continuous quantum phase transitions of the symmetry-breaking type in Dirac materials such as graphene and the surfaces of topological insulators are described by relativistic (2+1)-dimensional quantum field theories of the Gross-Neveu-Yukawa (GNY) type. We study the universal critical properties of the chiral Ising, XY, and Heisenberg GNY models perturbed by quenched random-mass disorder, both uncorrelated or with long-range power-law correlations. Using the replica method combined with a controlled triple epsilon expansion below four dimensions, we find a variety of new finite-randomness critical and multicritical points with nonzero Yukawa coupling between low-energy Dirac fields and bosonic order parameter fluctuations, and compute their universal critical exponents. Analyzing bifurcations of the renormalization-group flow, we find instances of the fixed-point annihilation scenario---continuously tuned by the power-law exponent of long-range disorder correlations and associated with an exponentially large crossover length---as well as the transcritical bifurcation and the supercritical Hopf bifurcation. The latter is accompanied by the birth of a stable limit cycle on the critical hypersurface, which represents the first instance of fermionic quantum criticality with emergent discrete scale invariance.