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.

在无序量子系统的统计力学中，一个重要但仍未解决的问题是了解淬灭的无序如何影响流动性费米子系统中的量子相变。在干净的极限下，通过Gross-Neveu-Yukawa（GNY）的相对论（2 + 1）维量子场论描述了狄拉克（Dirac）材料（例如石墨烯）和拓扑绝缘体表面中对称破坏类型的连续量子相变。 ）类型。我们研究了手性Ising，XY和Heisenberg GNY模型的普遍临界性质，这些模型受淬灭的随机质量紊乱的干扰，既不相关，也不与远距离幂律相关。将复制方法与可控的三ε扩展控制在四个维度以下相结合，我们发现了各种新的有限随机临界点和多临界点，它们在低能狄拉克场和玻色子阶跃参数波动之间具有非零的Yukawa耦合，并计算了它们的通用临界指数。分析重归一化组流的分叉，我们发现定点an灭情形的实例（通过远程无序关联的幂律指数不断调整，并与指数长的交叉长度相关联）以及跨临界分叉和超临界霍普夫分叉。后者伴随着临界超表面上稳定极限环的诞生，这代表了具有离散离散尺度不变性的费米子量子临界的第一个实例。