Related papers: Level statistics detect generalized symmetries
Symmetries are ubiquitous in real networks and often characterize network features and functions. Here we present a generalization of network symmetry called \emph{latent symmetry}, which is an extension of the standard notion of symmetry.…
Modulated symmetries are internal symmetries that act in a non-uniform, spatially modulated way and are generalizations of, for example, dipole symmetries. In this paper, we systematically study the gauging of finite Abelian modulated…
These are a set of lecture notes on generalized global symmetries in quantum field theory. The focus is on invertible symmetries with a few comments regarding non-invertible symmetries. The main topics covered are the basics of higher-form…
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of…
After having introduced the notion of universality in statistical mechanics and its importance for our comprehension of the macroscopic behavior of interacting systems, I review recent progress in the understanding of the scaling limit of…
In the article differential-difference (semi-discrete) lattices of hyperbolic type are investigated from the integrability viewpoint. More precisely we concentrate on a method for constructing generalized symmetries. This kind integrable…
We introduce a generalization of the q-analysis, which provides a novel non-parametric tool for the description and detection of log-periodic structures associated with discrete scale invariance. We use this generalized q-analysis to…
The statistics of particles and extended excitations, such as loops and membranes, are fundamental to modern condensed matter physics, high-energy physics, and quantum information science, yet a comprehensive lattice-level framework for…
$q$-charges describe the possible actions of a generalized symmetry on $q$-dimensional operators. In Part I of this series of papers, we describe $q$-charges for invertible symmetries; while the discussion of $q$-charges for non-invertible…
Ensembles of quantum chaotic systems are expected to exhibit energy eigenvalues with random-matrix-like level repulsion between pairs of energies separated by less than the inverse Thouless time. Recent research has shown that exact and…
Multilevel or hierarchical data structures can occur in many areas of research, including economics, psychology, sociology, agriculture, medicine, and public health. Over the last 25 years, there has been increasing interest in developing…
Projective symmetries are ubiquitous in quantum lattice models and can be leveraged to constrain their phase diagram and entanglement structure. In this paper, we investigate the consequences of projective algebras formed by non-invertible…
The formation of self-organized patterns and localized states are ubiquitous in Nature. Localized states containing trivial symmetries such as stripes, hexagons, or squares have been profusely studied. Disordered patterns with non-trivial…
Recently, it has been suggested that operational properties connected to quantum computation can be alternative indicators of quantum phase transitions. In this work we systematically study these operational properties in 1D systems that…
The statistical properties of the dynamics of energy levels are investigated in the case of two two-dimensional disordered quantum dot models with nearest neighbor hopping subjected to external time-dependent perturbations. While in the…
In the core of the vortex of a superconductor, energy levels appear inside the gap. We discuss here through a random matrix approach how these levels are broadened by impurities. It is first shown that the level statistics is governed by an…
We investigate the property of a spatial graph of having a leveled embedding and characterize the abstract graphs with this property. We show that all leveled embeddings are free and we compare leveled and paneled (also known as flat)…
Using a nonperturbative approach we examine the large frequency asymptotics of the two-point level density correlator in weakly disordered metallic grains. This allows us to study the behavior of the two-level structure factor close to the…
The main difficulty in high-dimensional anomaly detection tasks is the lack of anomalous data for training. And simply collecting anomalous data from the real world, common distributions, or the boundary of normal data manifold may face the…
Random matrix theory is a powerful tool for understanding spectral correlations inherent in quantum chaotic systems. Despite diverse applications of non-Hermitian random matrix theory, the role of symmetry remains to be fully established.…