Related papers: Topological state evolution by symmetry-breaking
We present a scheme to explicitly construct and classify general topological states jointly protected by an onsite symmetry group and a spatial symmetry group. We show that all these symmetry protected topological states can be…
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…
Clustering $\unicode{x2013}$ the tendency for neighbors of nodes to be connected $\unicode{x2013}$ quantifies the coupling of a complex network to its latent metric space. In random geometric graphs, clustering undergoes a continuous phase…
Topological phases have greatly improved our understanding of modern conception of phases of matter that go beyond the paradigm of symmetry breaking and are not described by local order parameters. Instead, characterization of topological…
In this paper, we explore the interplay between symmetry and fracton order, motivated by the analogous close relationship for topologically ordered systems. Specifically, we consider models with 3D planar subsystem symmetry, and show that…
We consider the existence of the topological entropy of shift spaces on a finitely generated semigroup whose Cayley graph is a tree. The considered semigroups include free groups. On the other hand, the notion of stem entropy is introduced.…
Band topology, or global wave-function structure that enforces novel properties in the bulk and on the surface of crystalline materials, is currently under intense investigations for both fundamental interest and its technological promises.…
We analyze the symmetry and topological features of a family of materials closely related to penta-graphene, derived from it by adsorption or substitution of different atoms. Our description is based on a novel approach, called topological…
Topological concepts have been employed to understand the ground states of many strongly correlated systems, but it is still quite unclear if and how topology manifests itself in the relaxation dynamics. Here we uncover emergent topological…
A convenient measure of a map or flow's chaotic action is the topological entropy. In many cases, the entropy has a homological origin: it is forced by the topology of the space. For example, in simple toral maps, the topological entropy is…
We use the persistent homology method of topological data analysis and dimensional analysis techniques to study data of syntactic structures of world languages. We analyze relations between syntactic parameters in terms of dimensionality,…
We propose a mechanism of topology-induced symmetry breaking, where certain local symmetry preserved by the Hamiltonian is explicitly broken in the eigenmodes of excitation due to nontrivial real-space topology. We demonstrate this…
In some scientific fields, a scaling is able to modify the topology of an observed object. Our goal in the present work is to introduce a new formalism adapted to the mathematical representation of this kind of phenomenon. To this end, we…
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous…
Two dimensional magnetic films with perpendicular magnetization spontaneously form magnetic domain patterns that evolve or undergo symmetry transformations as a function of temperature. When the system is driven from equilibrium by a rapid…
There are two prominent applications of the mathematical concept of topology to the physics of materials: band topology, which classifies different topological insulators and semimetals, and topological defects that represent immutable…
For $\alpha \in (1,2]$, the $\alpha$-stable graph arises as the universal scaling limit of critical random graphs with i.i.d. degrees having a given $\alpha$-dependent power-law tail behavior. It consists of a sequence of compact measured…
Motivated by the indications of high-Tc superconductivity in natural graphite enriched in the rhombohedral phase, we study the band structure of several stacking configurations that combine two of the three graphite structures as well as…
We use direct numerical simulations to study the evolution, or relaxation, of magnetic configurations to an equilibrium state. We use the full single-fluid equations of motion for a magnetized, non-resistive, but viscous fluid; and a…
The discovery of topological semimetals with multifold band crossings has opened up a new and exciting frontier in the field of topological physics. These materials exhibit large Chern numbers, leading to long double Fermi arcs on their…