相关论文: Robustness of Topological Order in the Toric Code …

Large language models suffer from "hallucinations"-logical inconsistencies induced by semantic noise. We propose that current architectures operate in a "Metric Phase," where causal order is vulnerable to spontaneous symmetry breaking.…

The interplay between dissipation and correlation can lead to novel emergent phenomena in open systems. Here we investigate ``steady-state topological order'' defined by the robust topological degeneracy of steady states, which is a…

We introduce a characterization of topological order based on bulk oscillations of the entanglement entropy and the definition of an `entanglement gap', showing that it is generally applicable to pure and disordered quantum systems. Using…

Topological classifications of quantum critical systems have recently attracted growing interest, as they go beyond the traditional paradigms of condensed matter and statistical physics. However, such classifications remain largely…

Symmetry protected topological order in one dimension leads to protected degeneracies between symmetry blocks of the reduced density matrix. In the presence of periodic driving, topological Floquet phases can be identified in terms of a…

The concept of topological phases has been generalized to higher-order topological insulators and superconductors with novel boundary states on corners or hinges. Meanwhile, recent experimental advances in controlling dissipation (such as…

We predict topologically robust zero energy bulk states in a disordered tight binding lattice. We explore a new kind of order and discuss that zero energy states exist in a system iff its Hamiltonian is noninvertible. We show that they are…

This paper investigates the stability properties and performance of super-twisting sliding-mode control loops subject to periodic perturbations. Although there exist conditions on the control gains that guarantee finite-time stability of…

The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped…

Systems displaying quantum topological order feature robust characteristics that are very attractive to quantum computing schemes. Topological quantum field theories have proven to be powerful in capturing the quintessential attributes of…

The entanglement properties of a class of topological stabilizer states, the so called \emph{topological color codes} defined on a two-dimensional lattice or \emph{2-colex}, are calculated. The topological entropy is used to measure the…

Three dimensional topological insulators embody a newly discovered state of matter characterized by conducting spin-momentum locked surface states that span the bulk band gap as demonstrated via spin-resolved ARPES measurements . This…

Nodal superconductors without inversion symmetry exhibit nontrivial topological properties, manifested by topologically protected flat-band edge states. Here we study the effects of breaking translational symmetry, crucial to the definition…

We investigate topological edge states in one-dimensional off-diagonal mosaic lattices, where nearest-neighbor hopping amplitudes are modulated periodically with period $\kappa>1$. Analytically, we demonstrate that discrete edge states…

We numerically investigate and experimentally demonstrate an in-situ topological band transition in a highly tunable mechanical system made of cylindrical granular particles. This system allows us to tune its inter-particle stiffness in a…

Insulating materials with dynamical spin degrees of freedom have recently emerged as viable conduits for spin flows. Transport phenomena harbored therein are, however, turning out to be much richer than initially envisioned. In particular,…

For classical discrete systems under constant composition, we re-examine how linear-nonlinear boundary in canonical ensemble, connecting a set of potential energy surface and that of microscopic configuration in thermodynamic equilibrium,…

In this work, we generalize several three-dimensional Z2 stabilizer models--including the X-cube model, the three-dimensional toric code, and Haah's code--to their ZN counterparts. Under periodic boundary conditions, we analyze their ground…

Several recent works have shown that state-of-the-art classifiers are vulnerable to worst-case (i.e., adversarial) perturbations of the datapoints. On the other hand, it has been empirically observed that these same classifiers are…

The goal of this paper is to analyze an intriguing phenomenon recently discovered in deep networks, namely their instability to adversarial perturbations (Szegedy et. al., 2014). We provide a theoretical framework for analyzing the…