Related papers: Topological Woodward-Hoffmann classification for c…
Path homology plays a central role in digraph topology and GLMY theory more general. Unfortunately, the computation of the path homology of a digraph $G$ is a two-step process, and until now no complete description of even the underlying…
As we all know the local topological properties of thermodynamical systems can be expressed by the winding numbers as the defects. The topological number that is the sum of all winding numbers can be used to classify the global topological…
Higher-order topological phases (HOTPs) hold gapped bulk bands and topological boundary states localized in boundaries with codimension higher than one. In this paper, we provide a unified construction and topological characterization of…
Structural disorder can improve the optical properties of metasurfaces, whether it is emerging from some large-scale fabrication methods, or explicitly designed and built lithographically. Correlated disorder, induced by a minimum…
We develop a theoretical framework for the classification and construction of symmetry protected topological (SPT) phases, which are a special class of zero-temperature phases of strongly interacting gapped quantum many-body systems that…
In this paper, we investigate signatures of topological phase transitions in interacting systems. We show that the key signature is the existence of a topologically protected level crossing, which is robust and sharply defines the…
We construct a topological invariant that classifies density matrices of symmetry-protected topological orders in two-dimensional fermionic systems. As it is constructed out of the previously introduced Uhlmann phase, we refer to it as the…
The search for pathways that optimize the formation of a particular target molecule in a reaction network is a key problem in many settings, including reactor systems. Chemical reaction networks are mathematically well represented as…
Techniques from higher categories and higher-dimensional rewriting are becoming increasingly important for understanding the finer, computational properties of higher algebraic theories that arise, among other fields, in quantum…
Ladder architectures are fruitful systems to realize topological phases of matter. Here we present a classification of ladder models giving rise to topological insulators. We identify six different types of topological ladder models, three…
The existence of topological order is frequently associated with strongly coupled quantum matter. Here, we demonstrate the existence of topological phases in classical systems of densely packed, hard, anisotropic polyhedrally shaped…
Topological constraints (TCs) between polymers determine the behaviour of complex fluids such as creams, oils and plastics. Most of the polymer solutions used every day life employ linear chains; their behaviour is accurately captured by…
Directional media, such as nematic liquid crystals and ferromagnets, are characterized by their topologically stabilized defects in directional order. In nematics, boundary conditions and surface-treated inclusions often create complex…
We investigate the topological classification of excitations in quadratic bosonic systems with an excitation band gap. Time-reversal, charge-conjugation, and parity symmetries in bosonic systems are introduced to realize a ten-fold symmetry…
Topological quantum optical states in one-dimensional (1D) quasiperiodic cold atomic chains are studied in this work. We propose that by introducing incommensurate modulations on the interatomic distances of 1D periodic atomic chains, the…
Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds…
In our previous work, Hopf cyclic cohomology in braided monoidal categories, we extended the formalism of Hopf cyclic cohomology due to Connes and Moscovici and the more general case of Hopf cyclic cohomology with coefficients to the…
Motivated by the abundance of symmetry breaking states in magic-angle twisted bilayer graphene and other two-dimensional materials, we study superconducting (SC) and charge orders in two-dimensional topological flat bands in the strong…
A stirring device consisting of a periodic motion of rods induces a mapping of the fluid domain to itself, which can be regarded as a homeomorphism of a punctured surface. Having the rods undergo a topologically-complex motion guarantees at…
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…