Related papers: Generalized multifractality at the spin quantum Ha…
Recently it has been demonstrated that the connectivity transition from microscopic connectivity to macroscopic connectedness, known as percolation, is generically announced by a cascade of microtransitions of the percolation order…
Multifractal dimensions allow for characterizing the localization properties of states in complex quantum systems. For ergodic states the finite-size versions of fractal dimensions converge to unity in the limit of large system size.…
We solve the problem of the spin quantum Hall transition on random networks using a mapping to classical percolation that focuses on the boundary of percolating clusters. Using tools of two-dimensional quantum gravity, we compute critical…
A multifractal phase transition is associated to a nonanalyticity in the generalised dimensions. We show that its occurrence is an artifact of the asymptotic scaling behaviour of integral moments and that it is not observed in an analysis…
In this work we launch a systematic theory of superconformal blocks for four-point functions of arbitrary supermultiplets. Our results apply to a large class of superconformal field theories including 4-dimensional models with any number…
In circuit-based quantum state preparation, qubit loss and coherent errors are circuit imperfections that imperil the formation of long-range entanglement beyond a certain threshold. The critical theory at the threshold is a continuous…
In this paper we investigate the universality and scaling properties of the well-known quantities in classical statistical mechanics near the quantum phase transition point. We show that transverse susceptibility and derivatives of…
The wavefunctions of a disordered two-dimensional electron gas at the quantum-critical Anderson transition are predicted to exhibit multifractal scaling in their real space amplitude. We experimentally investigate the appearance of these…
The multifractality of the critical eigenstate at the metal to insulator transition (MIT) in the three-dimensional Anderson model of localization is characterized by its associated singularity spectrum f(alpha). Recent works in 1D and 2D…
A two dimensional disordered system of non-interacting fermions in a homogeneous magnetic field is investigated numerically. By introducing a new magnetic gauge, we explore the renormalization group (RG) flow of the longitudinal and Hall…
It is an outstanding goal to unveil the key features of quantum dynamics at eigenstate transitions. Focusing on quadratic fermionic Hamiltonians that exhibit localization transitions, we identify physical observables that exhibit…
The level curvature distribution function is studied both analytically and numerically for the case of T-breaking perturbations over the orthogonal ensemble. The leading correction to the shape of the curvature distribution beyond the…
We investigate boundary multifractality of critical wave functions at the Anderson metal-insulator transition in two-dimensional disordered non-interacting electron systems with spin-orbit scattering. We show numerically that multifractal…
The coupling space of perceptrons with continuous as well as with binary weights gets partitioned into a disordered multifractal by a set of $p=\gamma N$ random input patterns. The multifractal spectrum $f(\alpha)$ can be calculated…
Understanding the fluctuations of observables is one of the main goals in science, be it theoretical or experimental, quantum or classical. We investigate such fluctuations when only a subregion of the full system can be observed, focusing…
The nature of the critical point of the Anderson transition in high magnetic fields is discussed with an emphasis on scale invariance and universality of the critical exponent. Special attention is paid to the distribution function of the…
We present a scaling theory of the many-body localisation transition in terms of emergent, characteristic energyscales. The analysis is based on the decomposition of the eigenstates in the basis of trivially localised states, resolved in…
Self-affine morphology of random interfaces governs their functionalities across tribological, geological, (opto-)electrical and biological applications. However, the knowledge of how energy carriers or generally classical/quantum waves…
We obtain a ``mean field'' scaling flow of the longitudinal and the Hall conductivities in the fractional quantum Hall regime. Using the composite fermion picture and assuming that the composite fermions follow the Khmelnitskii-Pruisken…
We define a class of random measures, spatially independent martingales, which we view as a natural generalisation of the canonical random discrete set, and which includes as special cases many variants of fractal percolation and Poissonian…