Related papers: Topological Matter and Fractional Entangled Quantu…
The chiral soliton lattice is an array of topological solitons realized as ground states of QCD at finite density under strong magnetic fields or rapid rotation, and chiral magnets with an easy-plane anisotropy. In such cases, topological…
The motion of a conducting electron in a quantum dot with one or several dislocations in the underlying crystal lattice is considered in the continuum picture, where dislocations are represented by torsion of space. The possible effects of…
Topological matter has become one of the most important subjects in contemporary condensed matter physics. Here, I would like to provide a pedagogical review explaining some of the main ideas, which were pivotal in establishing topological…
Topological textures in magnetically ordered materials are important case studies for fundamental research with promising applications in data science. They can also serve as photonic elements to mold electromagnetic fields endowing them…
We derive for Bohmian mechanics topological factors for quantum systems with a multiply-connected configuration space Q. These include nonabelian factors corresponding to what we call holonomy-twisted representations of the fundamental…
Geometrical and topological phases play a fundamental role in quantum theory. Geometric phases have been proposed as a tool for implementing unitary gates for quantum computation. A fractional topological phase has been recently discovered…
In this paper, we address a foundational challenge in quantum field theory on curved spacetime by developing a consistent framework within loop quantum gravity. We introduce a methodology for defining meaningful superpositions of quantum…
In topological phases of matter, the interplay between intrinsic topological order and global symmetry is an interesting task. In the study of topological orders with discrete global symmetry, an important systematic approach is the…
Topological principles constitute at present an integral component of condensed matter physics, permeating the modern characterization of electronic states while also guiding materials design. In this brief Perspective, I highlight three…
Crystalline symmetries give rise to topological invariants that can distinguish quantum phases of matter. Understanding these in strongly interacting systems is an ongoing research direction requiring non-perturbative methods. Recent…
Topology in photonics comes in two distinct flavors: global and local. Global topology considers invariants that are obtained by integrating over the energy band, whereas local topology considers defects, typically vortices, in the…
Topological photonics provides a novel platform to explore topological physics beyond traditional electronic materials and stimulates promising applications in topologically protected light transport and lasers. Classical degrees of freedom…
By virtue of harmonic maps on two-dimensional spheres (S$^{2}$), a topological quantization in spacetime is proposed. The discrete character of all physical quantities follows naturally. A Schwarzschild black hole, non-black hole and…
The quantum geometry of Bloch wavefunctions,encoded in the Berry curvature and quantum metric, is believed to be a decisive ingredient in stabilizing fractional quantum anomalous Hall (FQAH) effect(i.e., fractional Chern insulator, FCI, at…
Advanced vector imaging techniques provide us with 3D maps of magnetization fields in which topological concepts can be directly applied to describe real-space experimental textures in non-ideal geometries. Here, the 3D magnetization of a…
These notes review a description of quantum mechanics in terms of the topology of spaces, basing on the axioms of Topological Quantum Field Theory and path integral formalism. In this description quantum states and operators are encoded by…
In a seminal paper Haldane conjectured that topological phenomena are not particular to quantum systems, and indeed experiments realized unidirectional, backscattering-free edge modes with electromagnetic waves. This raises two immediate…
Topological states of matter, as quantum Hall systems or topological insulators, cannot be distinguished from ordinary matter by local measurements in the bulk of the material. Instead, global measurements are required, revealing…
Quantum spin-Hall effect, a manifestation of topological properties that govern the behavior of surface states, was studied intensively in condensed matter physics resulting in the discovery of topological insulators. The quantum spin-Hall…
The quantum geometry of Bloch wavefunctions underpins a wealth of emergent phenomena in quantum materials. Its imaginary part, the Berry curvature, has long been recognized as a key source for hallmark effects such as quantum Hall and…