Related papers: Graph Theory Data for Topological Quantum Chemistr…
Besides the plenty of applications of graphene allotropes in condensed matter and nanotechnology, we argue that graphene sheets might be engineered to support room-temperature topological quantum processing of information. The argument is…
Topological phases of matter give rise to exotic physics that can be leveraged for next generation quantum computation and spintronic devices. Thus, the search for topological phases and the quantum states that they exhibit have become the…
Topology is a fundamental aspect of quantum physics, and it has led to key breakthroughs and results in various fields of quantum materials. In condensed matters, this has culminated in the recent discovery of symmetry-protected topological…
We consider the Dirac equation on periodic networks (quantum graphs). The self-adjoint quasi periodic boundary conditions are derived. The secular equation allowing us to find the energy spectrum of the Dirac particles on periodic quantum…
We develop random graph models where graphs are generated by connecting not only pairs of vertices by edges but also larger subsets of vertices by copies of small atomic subgraphs of arbitrary topology. This allows the for the generation of…
Motivated by new capabilities to realise artificial gauge fields in ultracold atomic systems, and by their potential to access correlated topological phases in lattice systems, we present a new strategy for designing topologically…
We study a family of closed quantum graphs described by one singular vertex of order n=4. By suitable choice of the parameters specifying the singular vertex, we can construct a closed sequence of paths in the parameter space that…
The spin-orbit coupling field, an atomic magnetic field inside a Kramer's system, or discrete symmetries can create a topological torus in the Brillouin Zone and provide protected edge or surface states, which can contain relativistic…
Previous symmetry-based database searches have already revealed ubiquitous band topology in nature, while the destiny of band topology under symmetry-breaking is yet to be studied comprehensively. Here we first develop a framework allowing…
Geometric, topological and graph theory modeling and analysis of biomolecules are of essential importance in the conceptualization of molecular structure, function, dynamics, and transport. On the one hand, geometric modeling provides…
Topological properties of a periodic condensed matter system are global features of its Brillouin zone (BZ). In contrast, the validity of effective low energy theories is usually limited to the vicinity of a high symmetry point in the BZ.…
The use of topology for visualisation applications has become increasingly popular due to its ability to summarise data at a high level. Criticalities in scalar field data are used by visualisation methods such as the Reeb graph and contour…
Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. In many cases the morphology of coexisting phases is crucially linked to the function of the separated…
Nowadays, the coupling of electronic structure and machine learning techniques serves as a powerful tool to predict chemical and physical properties of a broad range of systems. With the aim of improving the accuracy of predictions, a large…
Formation of a molecular network from multifunctional precursors is modelled with a random graph process. The random graph model favours reactivity for monomers that are positioned close in the network topology, and disfavours reactivity…
We combine space group representation theory together with scanning of closed subdomains of the Brillouin zone with Wilson loops to algebraically determine global band structure topology. Considering space group #19 as a case study, we show…
Graph structures are ubiquitous throughout the natural sciences. Here we consider graph-structured quantum data and describe how to carry out its quantum machine learning via quantum neural networks. In particular, we consider training data…
We discuss and demonstrate an unsupervised machine-learning procedure to detect topological order in quantum many-body systems. Using a restricted Boltzmann machine to define a variational ansatz for the low-energy spectrum, we sample wave…
The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained (in part) from momentum space. Recently, Real Space…
In recent work, the authors developed a simple method of constructing topological spaces from certain well-behaved partially ordered sets -- those coming from sequences of relations between finite sets. This method associates a given poset…