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For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…

Symmetry-protected topological (SPT) phases exhibit nontrivial order if symmetry is respected but are adiabatically connected to the trivial product phase if symmetry is not respected. However, unlike the symmetry-breaking phase, there is…

Discovering a suitable coordinate transformation for nonlinear systems enables the construction of simpler models, facilitating prediction, control, and optimization for complex nonlinear systems. To that end, Koopman operator theory offers…

The one-dimensional $p$-wave superconductor proposed by Kitaev has long been a classic example for understanding topological phase transitions through various methods, such as examining Berry phase, edge states of open chains and, in…

The capabilities of image probe experiments are rapidly expanding, providing new information about quantum materials on unprecedented length and time scales. Many such materials feature inhomogeneous electronic properties with intricate…

How much information is stored in the ground-state of a system without \emph{any symmetry} and how can we extract it? This question is investigated by analyzing the behavior of a topological Chern Insulator (CI) in the presence of disorder,…

Smart meters provide relevant information for impedance identification, but they lack global phase alignment and internal network nodes are often unobserved. A few methods for this setting were developed, but they have requirements on data…

The recent advances in machine learning algorithms have boosted the application of these techniques to the field of condensed matter physics, in order e.g. to classify the phases of matter at equilibrium or to predict the real-time dynamics…

Among many types of quantum entanglement properties, the entanglement spectrum provides more abundant information than other observables. Exact diagonalization and density matrix renormalization group method could handle the system in…

A rigorous analysis is presented for the entanglement spectrum of quantum many-body states possessing a higher-form group-representation symmetry generated by topological Wilson loops, which is generally non-invertible. A general framework…

The systematic diagnosis of band topology enabled by the method of "symmetry indicators" underlies the recent advances in the search for new materials realizing topological crystalline insulators. Such an efficient method has been missing…

Complex networks play a fundamental role in understanding phenomena from the collective behavior of spins, neural networks, and power grids to the spread of diseases. Topological phenomena in such networks have recently been exploited to…

Topological phase transitions can be remarkably induced purely by manipulating gain and loss mechanisms, offering a novel approach to engineering topological properties. Recent theoretical studies have revealed gain-loss-induced topological…

The search for materials with topological properties is an ongoing effort. In this article we propose a systematic statistical method supported by machine learning techniques that is capable of constructing topological models for a generic…

In this paper, we study the problem of using representation learning to assist information diffusion prediction on graphs. In particular, we aim at estimating the probability of an inactive node to be activated next in a cascade. Despite…

This paper proposes a neural framework for power and timing prediction of multi-stage data path, distinguishing itself from traditional lib-based analytical methods dependent on driver characterization and load simplifications. To the best…

Certain band insulators allow for the adiabatic pumping of quantized charge or spin for special time-dependences of the Hamiltonian. These "topological pumps" are closely related to two dimensional topological insulating phases of matter…

We generalize the Hamiltonian Monte Carlo algorithm with a stack of neural network layers and evaluate its ability to sample from different topologies in a two dimensional lattice gauge theory. We demonstrate that our model is able to…

These lecture notes on entanglement in topological systems are part of the 48th IFF Spring School 2017 on Topological Matter: Topological Insulators, Skyrmions and Majoranas at the Forschungszentrum Juelich, Germany. They cover a short…

Topological order in a 2d quantum matter can be determined by the topological contribution to the entanglement R\'enyi entropies. However, when close to a quantum phase transition, its calculation becomes cumbersome. Here we show how…