Related papers: Knotting and higher order linking in physical syst…
This note is a survey on the topology of hyperplane arrangements. We mainly focus on the relationship between topology and the real structure, such as adjacent relations of chambers and stratifications related to real structures.
Knotted solutions to electromagnetism and fluid dynamics are investigated, based on relations we find between the two subjects. We can write fluid dynamics in electromagnetism language, but only on an initial surface, or for linear…
We discuss the possibility of the existence of finite algorithms that may give distinct knot classes. In particular we present two attempts for such algorithms which seem promising, one based on knot projections on a plane, the other on…
Topological orders are a prominent paradigm for describing quantum many-body systems without symmetry-breaking orders. We present a topological quantum field theoretical (TQFT) study on topological orders in five-dimensional spacetime…
We discuss quantum mechanical and topological aspects of nonabelian monopoles. Related recent results on nonabelian vortices are also mentioned.
We argue that the local violation of P invariance in heavy ion collisions is a consequence of the long range topological order which is inherent feature of strongly coupled QCD. A similar phenomenon is known to occur in some topologically…
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…
Here we show the connection between topological order and the geometric entanglement, as measured by the logarithm of the overlap between a given state and its closest product state of blocks, for the topological universality class of the…
Knots and links are fundamental topological objects play a key role in both classical and quantum fluids. In this research, we propose a novel scheme to generate torus vortex knots and links through the reconnections of vortex rings…
Recently realized higher order topological insulators have taken a surge of interest among the theoretical and experimental condensed matter community. The two-dimensional second order topological insulators give rise to zero-dimensional…
We extend the list of known band structure topologies to include a large family of hyperbolic nodal links and knots, occurring both in conventional Hermitian systems where their stability relies on discrete symmetries, and in the…
In recent years, new algorithms and cryptographic protocols based on the laws of quantum physics have been designed to outperform classical communication and computation. We show that the quantum world also opens up new perspectives in the…
In this paper we explore how non trivial boundary conditions could influence the entanglement entropy in a topological order in 2+1 dimensions. Specifically we consider the special class of topological orders describable by the quantum…
This is a survey article for the Encyclopedia of Mathematical Physics, 2nd Edition. Topological defects are described in the context of the 2-dimensional Ising model on the lattice, in 2-dimensional quantum field theory, in topological…
Coupled-wire constructions have been widely applied to quantum Hall systems and symmetry-protected topological (SPT) phases. In this Letter, we use the coupled one-dimensional nonchiral Luttinger liquids with domain-wall structured mass…
We survey some of the connections linking complex dynamics to other fields of mathematics and science. We hope to show that complex dynamics is not just interesting on its own but also has value as an applicable theory.
In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of…
We consider the links between consistent and approximate descriptions of the quantum-classical systems, i.e. systems are composed of two interacting subsystems, one of which behaves almost classically while the other requires a quantum…
We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…
We revisit the connection between entanglement entropy and quantum metric in topological lattice systems, and provide an elegant and concise proof of this connection. In gapped two-dimensional lattice models with well-defined tight-binding…