Related papers: Quantitative analytical theory for disordered noda…
Quantifying the level of atomic disorder within materials is critical to understanding how evolving local structural environments dictate performance and durability. Here, we leverage graph neural networks to define a physically…
We develop an efficient numerical method to study the quantum critical behavior of disordered systems with $\mathcal{O}(N)$ order-parameter symmetry in the large$-N$ limit. It is based on the iterative solution of the large$-N$ saddle-point…
It is commonly believed that a non-interacting disordered electronic system can undergo only the Anderson metal-insulator transition. It has been suggested, however, that a broad class of systems can display disorder-driven transitions…
Pursuing complementary field-theoretic and numerical methods, we here paint the global phase diagram of a three-dimensional dirty Weyl system. The generalized Harris criterion, augmented by a perturbative renormalization-group (RG) analysis…
We study the long-time asymptotics of a certain class of nonlinear diffusion equations with time-dependent diffusion coefficients which arise, for instance, in the study of transport by randomly fluctuating velocity fields. Our primary goal…
The renormalization group method enables one to improve the properties of the QCD perturbative power series in the ultraviolet region. However, it ultimately leads to the unphysical singularities of observables in the infrared domain. The…
We introduce a class of variational states to describe quantum many-body systems. This class generalizes matrix product states which underly the density-matrix renormalization group approach by combining them with weighted graph states.…
Three dimensional Dirac semimetals are stable against weak potential disorder, but not against strong disorder. In the language of renormalization group, such stability stems from the irrelevance of weak disorder in the vicinity of the…
Asymptotical behavior of the distribution function of local density of states (LDOS) in disordered metallic samples is studied with making use of the supersymmetric $\sigma$--model approach, in combination with the saddle--point method. The…
In this work we explore the effects of nonlinearity on three-dimensional topological phases. Of particular interest are the so-called Weyl semimetals, known for their Weyl nodes, i.e., point-like topological charges which always exist in…
Constructing an effective field theory in terms of doped magnetic impurities (described by an O(3) vector model with a random mass term), itinerant electrons of spin-orbit coupled semiconductors (given by a Dirac theory with a relatively…
We review current progress in the functional renormalization group treatment of disordered systems. After an elementary introduction into the phenomenology, we show why in the context of disordered systems a functional renormalization group…
Finite temperature Euclidean two-point functions in quantum mechanics or quantum field theory are characterized by a discrete set of Fourier coefficients $G_{k}$, $k\in\mathbb Z$, associated with the Matsubara frequencies $\nu_{k}=2\pi…
Quenched disorder in graphene is characterized by 5 constants and experiences the logarithmic renormalization even from the spatial scales smaller than the Fermi wavelength. We derive and solve renormalization group equations (RGEs)…
We perform a complete classification of two-band $\bk\cdot\mathbf{p}$ theories at band crossing points in 3D semimetals with $n$-fold rotation symmetry and broken time-reversal symmetry. Using this classification, we show the existence of…
We consider the disorder-induced correction to the minimal conductance of an anisotropic two-dimensional Dirac node or a three-dimensional Weyl node. An analytical expression is derived for the correction $\delta G$ to the conductance of a…
In disordered Weyl semimetals, mechanisms of topological origin lead to novel mechanisms of transport, which manifest themselves in unconventional types of electromagnetic response. Prominent examples of transport phenomena particular to…
In this paper, the average density of states (ADOS) with a binary alloy disorder in disordered graphene systems are calculated based on the recursion method. We observe an obvious resonant peak caused by interactions with surrounding…
Taking into account the interplay between the disorder and Coulomb interaction, the phase diagram of three-dimensional anisotropic Weyl semimetal is studied by renormalization group theory. Weak disorder is irrelevant in anisotropic Weyl…
Many-body electron-electron interaction effects are theoretically considered in monolayer graphene from a continuum effective field-theoretic perspective by going beyond the standard leading-order perturbative renormalization group (RG)…