Related papers: Knot Topology in Quantum Spin System
Entanglement represents a pure quantum effect involving two or more particles. Spin systems are good candidates for studying this effect and its relation with other collective phenomena ruled by quantum mechanics. While the presence of…
We investigate the relation between the topology of a nucleon and its spin composition. We approach this question in (1+1) dimensional single-flavor QCD with a large number of color. In this limit the theory can be shown to be dual to the…
For many materials, a precise knowledge of their dispersion spectra is insufficient to predict their ordered phases and physical responses. Instead, these materials are classified by the geometrical and topological properties of their…
In this paper, knotted objects (RS vortices) in the theory of topological phase singularity in electromagnetic field have been investigated in details. By using the $\phi$-mapping topological current theory proposed by Prof. Duan, we…
We present a new paradigm for three dimensional chaos, and specifically for the Lorenz equations. The main difficulty in these equations and for a generic flow in dimension three is the existence of singularities. We show how to use knot…
This is an introductory review of the physics of topological quantum matter with cold atoms. Topological quantum phases, originally discovered and investigated in condensed matter physics, have recently been explored in a range of different…
We describe a scheme that enables a strong coherent coupling between a topological qubit and the quantized motion of a magnetized nanomechanical resonator. This coupling is achieved by attaching an array of magnetic tips to a namomechanical…
The nontrivial topology of spin systems such as skyrmions in real space can promote complex electronic states. Here, we provide a general viewpoint at the emergence of topological electronic states in spin systems based on the methods of…
The interaction between spins in coupled quantum dots is revealed in distinct fine structure patterns in the measured optical spectra of InAs/GaAs double quantum dot molecules containing zero, one, or two excess holes. The fine structure is…
Here, we reveal our recent progress on a geometrical approach of quantum physics and topological crystals linking with Dirac magnetic monopoles and gauge fields through classical electrodynamics. The Bloch sphere of a quantum spin-1/2…
Structure in quantum entanglement entropy is often leveraged to focus on a small corner of the exponentially large Hilbert space and efficiently parameterize the problem of finding ground states. A typical example is the use of matrix…
Recently topological states of matter have witnessed a new physical phenomenon where both edge modes and gapless bulk coexist at topological quantum criticality. The presence and absence of edge modes on a critical line can lead to an…
Motivated by the goal to give the simplest possible microscopic foundation for a broad class of topological phases, we study quantum mechanical lattice models where the topology of the lattice is one of the dynamical variables. However, a…
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…
Virtual knot theory is a generalization (discovered by the author in 1996) of knot theory to the study of all oriented Gauss codes. (Classical knot theory is a study of planar Gauss codes.) Graph theory studies non-planar graphs via…
In topological quantum computing, information is encoded in "knotted" quantum states of topological phases of matter, thus being locked into topology to prevent decay. Topological precision has been confirmed in quantum Hall liquids by…
We find further evidence for the conjecture relating large N Chern-Simons theory on S^3 with topological string on the resolved conifold geometry by showing that the Wilson loop observable of a simple knot on S^3 (for any representation)…
The quantum walk is a dynamical protocol which describes the motion of spinful particles on a lattice. Also, it has been demonstrated to be a powerful platform to explore topological quantum matter. Recently, the quantum walk in coherent…
Topology is an important degree of freedom in characterizing electronic systems. Recently, it also brings new theoretical frontiers and many potential applications in photonics. However, the verification of the topological nature is highly…
The spin network simulator model represents a bridge between (generalized) circuit schemes for standard quantum computation and approaches based on notions from Topological Quantum Field Theories (TQFT). More precisely, when working with…