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

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.

arXiv comment50 pages, 15 figures, 1 table; v2: published version

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• Emergent space-time supersymmetry at disorder quantum critical point
• SO(4) multicriticality of two-dimensional Dirac fermions
• Absence of SO(4) quantum criticality in Dirac semimetals at two-loop order
• Fermion enhanced first-order phase transition and chiral Gross-Neveu tricritical point
• Spatially Random Disorder in Unitary Fermion System in $(4-\epsilon )$-Dimensions and Effective Action at Finite Temperature
• Crumpled-to-flat transition of quenched disordered membranes at two-loop order
• Interplay of interactions and disorder at the charge-density wave transition of two-dimensional Dirac semimetals