Related papers: Graph Theory Data for Topological Quantum Chemistr…

The interplay between topology and nonlinearity represents a central challenge in modern physics. Here, we investigate this interplay by considering a synthetic Su-Schrieffer-Heeger lattice with all-to-all nonlocal interactions. We find…

Topological photonics is developed based on the analogy of Schr\"{o}dinger equation which is mathematically reduced to a standard eigenvalue equation. Notably, several photonic systems are beyond the standard topological band theory as they…

The topological mechanics is a perfect tool that can bridge the gap between the quantum and Newtonian physics and mechanics of materials. It requires discrete models of the material with analogies with the topological characteristics of…

Topologically protected edge states have been extensively studied in systems characterized by the topological invariants in band gaps (also called line gaps). In this study, we unveil a whole new form of edge states that transcends the…

The monography examines the problem of constructing a group of automorphisms of a graph. A graph automorphism is a mapping of a set of vertices onto itself that preserves adjacency. The set of such automorphisms forms a vertex group of a…

We show a surprising link between experimental setups to realize high-dimensional multipartite quantum states and Graph Theory. In these setups, the paths of photons are identified such that the photon-source information is never created.…

We explain why, in a configuration space that is multiply connected, i.e., whose fundamental group is nontrivial, there are several quantum theories, corresponding to different choices of topological factors. We do this in the context of…

Topology is being widely adopted to understand and to categorize quantum matter in modern physics. The nexus of topology orders, which engenders distinct quantum phases with benefits to both fundamental research and practical applications…

We analyze the nonlinear optics of quasi one-dimensional quantum graphs and manipulate their topology and geometry to generate for the first time nonlinearities in a simple system approaching the fundamental limits of the first and second…

Recent advancements in the field of topological band theory have significantly contributed to our understanding of intriguing topological phenomena observed in various classical and quantum systems, encompassing both wave and dissipative…

We outline an approach to endow a plain vanilla material with topological properties by creating topological bands in stacks of manifestly nontopological atomically thin materials. The approach is illustrated with a model system comprised…

The recently developed theory of topological quantum chemistry (TQC) has built a close connection between band representations in momentum space and orbital characters in real space. It provides an effective way to diagnose topological…

To provide a phenomenological theory for the various interesting transitions in restructuring networks we employ a statistical mechanical approach with detailed balance satisfied for the transitions between topological states. This enables…

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials,…

Quantum self-oscillatory phases are ubiquitous in driven-dissipative systems. Classically, each phase is defined by its flow pattern and how stationary sets organize phase space (e.g. fixed points and limit cycles), with transitions…

The dimensionality of kernels for Lindbladian superoperators is of physical interest in various scenarios out of equilibrium, for example in mean-field methods for driven-dissipative spin lattice models that give rise to phase diagrams with…

Topological phases for free fermions in systems with crystal symmetry are classified by the topology of the valence band viewed as a vector bundle over the Brillouin zone. Additional symmetries, such as crystal symmetries which act…

The method of the space dependent basis is applied to study electronic spinors in a crystal. The crystal in the momentum space is described by the Brillouine zone which might contains obstructions or degeneracies for which requires…

Non-Hermitian matrices are ubiquitous in the description of nature ranging from classical dissipative systems, including optical, electrical, and mechanical metamaterials, to scattering of waves and open quantum many-body systems. Seminal…

Topology, a mathematical concept, has recently become a popular and truly transdisciplinary topic encompassing condensed matter physics, solid state chemistry, and materials science. Since there is a direct connection between real space,…