Related papers: Elements, topology, and T-shirts
Many systems in nature and the synthetic world involve ordered arrangements of units on two-dimensional surfaces. We review here the fundamental role payed by both the topology of the underlying surface and its detailed curvature. Topology…
We investigate spectral properties of quantum graphs in the form of a periodic chain of rings with a connecting link between each adjacent pair, assuming that wave functions at the vertices are matched through conditions manifestly…
We develop a scheme to make exactly solvable gauge theories whose electric flux lines host (1+1)-dimensional topological phases. We use this exact `decorated-string-net' framework to construct several classes of interesting models. In…
A periodic weave is the lift of a particular link embedded in a thickened surface to the universal cover. Its components are infinite unknotted simple open curves that can be partitioned in at least two distinct sets of threads. The…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Topological Interlocking assemblies are arrangements of blocks kinematically constrained by a fixed frame, such that all rigid body motions of each block are constrained only by its permanent contact with other blocks and the frame. In the…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
The Nielsen-Thurston theory of surface diffeomorphisms shows that useful dynamical information can be obtained about a surface diffeomorphism from a finite collection of periodic orbits.In this paper, we extend these results to homoclinic…
We propose a link prediction algorithm that is based on spring-electrical models. The idea to study these models came from the fact that spring-electrical models have been successfully used for networks visualization. A good network…
In this work, we reconsider the study of 2D materials involving double lattice structures associated with periodic polygons. In tessellated periodic representation, it appears two periodic polygons of $k$ sides of unequal side lengths at…
Topological materials have become the focus of intense research in recent years, since they exhibit fundamentally new physical phenomena with potential applications for novel devices and quantum information technology. One of the hallmarks…
Initiated by the discovery of topological insulators, topologically non-trivial materials have attracted immense interest in the physics community in the past decade. One of the latest additions to the field, the material class of…
In this article we investigate the possibility of generating piezoelectric orbital polarization in graphene-like systems which are deformed periodically. We start with discrete two-level models which depend on control parameters; in this…
The adhesion approximation is a simple analytical model suggested for explanation of the major geometrical features of the observed structure in the galaxy distribution on scales from 1 to (a few)x100/h Mpc. It is based on Burgers' equation…
We discuss some bulk-surfaces gapped Hamiltonians on a lattice with corners and propose a periodic table for topological invariants related to corner states aimed at studies of higher-order topological insulators. Our table is based on four…
We explore the applicability of the transcorrelated method to the elements in the second row of the periodic table. We use transcorrelated Hamiltonians in conjunction with full configuration interaction quantum Monte Carlo and coupled…
We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our…
Elementary band representations are the fundamental building blocks of atomic limit band structures. They have the defining property that at partial filling they cannot be both gapped and trivial. Here, we give two examples -- one each in a…
Given a sequence of oriented links L^1,L^2,L^3,... each of which has a distinguished, unknotted component, there is a decomposition of the 3-sphere naturally associated to it, which is constructed as the components of the intersection of an…
A general strategy of alternated slide construction to craft topological metals is proposed, where there is a relative slide between the odd and even chains in the trivial spinless quantum wire array. Firstly, taking the three-leg ladder as…