Related papers: Knot Topology in Quantum Spin System
Networked systems display complex patterns of interactions between a large number of components. In physical networks, these interactions often occur along structural connections that link components in a hard-wired connection topology,…
Classical knot theory deals with {\em diagrams} and {\em invariants}. By means of horizontal {\em trisecants}, we construct a new theory of classical braids with invariants valued in {\em pictures}. These pictures are closely related to…
Networks based on entangled quantum systems enable interesting applications in quantum information processing and the understanding of the resulting quantum correlations is essential for advancing the technology. We show that the theory of…
We study the ground-state entanglement in systems of spins forming the boundary of a quantum spin network in arbitrary geometries and dimensionality. We show that as long as they are weakly coupled to the bulk of the network, the surface…
The spin network quantum simulator relies on the su(2) representation ring (or its q-deformed counterpart at q= root of unity) and its basic features naturally include (multipartite) entanglement and braiding. In particular, q-deformed spin…
Magnetically ordered materials tend to support bands of coherent propagating spin wave, or magnon, excitations. Topologically protected surface states of magnons offer a new path towards coherent spin transport for spintronics applications.…
Non-perturbative approaches to quantum gravity call for a deep understanding of the emergence of geometry and locality from the quantum state of the gravitational field. Without background geometry, the notion of distance should entirely…
We use the topological quantum field theory description of states in Chern-Simons theory to discuss the relation between spacetime connectivity and entanglement, exploring the paradigm entanglement=topology. We define a special class of…
We investigate quantum phase transitions (QPTs) in spin chain systems characterized by local Hamiltonians with matrix product ground states. We show how to theoretically engineer such QPT points between states with predetermined properties.…
The fundamental problem of knot theory is to know whether two knots are equivalent or not. As a tool to prove that two knots are different, mathematicians have developed various invariants. Knots invariants are just functions that can be…
We examine several well known quantum spin models and categorize behavior of pairwise entanglement at quantum phase transitions. A unified picture on the connection between the entanglement and quantum phase transition is given.
We study the many-body physics of different quantum systems using a hierarchy of correlations, which corresponds to a generalization of the $1/\mathcal{Z}$ hierarchy. The decoupling scheme obtained from this hierarchy is adapted to…
The topology of entanglement in multipartite states with translational invariance is discussed in this article. Two global features are foundby which one can distinguish distinct states. These are the cyclic unit and the quantised geometric…
Entanglement constitutes one of the key concepts in quantum mechanics and serves as an indispensable tool in the understanding of quantum many-body systems. In this work, we perform extensive numerical investigations of extensive…
Motivated by the idea that, in the background-independent framework of a Quantum Theory of Gravity, entanglement is expected to play a key role in the reconstruction of spacetime geometry, we investigate the possibility of using the…
The physics of interacting integer-spin chains has been a topic of intense theoretical interest, particularly in the context of symmetry-protected topological phases. However, there has not been a controllable model system to study this…
Topological phases are often characterized by special edge states confined near the boundaries by an energy gap in the bulk. On raising temperature, these edge states are lost in a clean system due to mobile thermal excitations. Recently…
Large-scale quantum networks, necessary for distributed quantum information processing, are posited to have quantum entangled systems between distant network nodes. The extent and quality of distributed entanglement in a quantum network,…
We present two models for the space of knots which have endpoints at fixed boundary points in a manifold with boundary, one model defined as an inverse limit of spaces of maps between configuration spaces and another which is cosimplicial.…
We study how topological crystalline defects--dislocations--reshape the real-space quantum geometric tensor and act as tunable sources of quantum geometry. We show that dislocations strongly enhance the quantum metric, establishing a direct…