Related papers: Topological Properties and Characterizations
This article is meant as a gentle introduction to the "topological terms" that often play a decisive role in effective theories describing topological quantum effects in condensed matter systems. We first take up several prominent examples,…
We study the global and local topological properties of multi-lepton patterns reconstructed at the detectors. We investigate the sensitivity of Forman Ricci curvature distributions and persistent homology features to kinematic cuts,…
We introduce a generalization of conventional lattice gauge theory to describe fracton topological phases, which are characterized by immobile, point-like topological excitations, and sub-extensive topological degeneracy. We demonstrate a…
For particles confined to two dimensions, any curvature of the surface affects the structural, kinetic and thermodynamic properties of the system. If the curvature is non-uniform, an even richer range of behaviours can emerge. Using a…
We determine which connected surfaces can be partitioned into topological circles. There are exactly seven such surfaces up to homeomorphism: those of finite type, of Euler characteristic zero, and with compact boundary components. As a…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
Aspects of the theory of characteristic modes, based on their variational formulation, are presented and an explicit form of a related functional, involving only currents in a spatial domain, is derived. The new formulation leads to deeper…
For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at…
We characterize structures such as monotonicity, convexity, and modality in smooth regression curves using persistent homology. Persistent homology is a key tool in topological data analysis that detects higher-dimensional topological…
We discuss the appearance of fractional topological phases on cyclic evolutions of entangled qudits. The original result reported in Phys. Rev. Lett. \textbf{106}, 240503 (2011) is detailed and extended to qudits of different dimensions.…
Physical systems are frequently modeled as sets of points in space, each representing the position of an atom, molecule, or mesoscale particle. As many properties of such systems depend on the underlying ordering of their constituent…
We explore one-dimensional fermionic symmetry-protected topological (SPT) phases related by the crystalline equivalence principle. In particular, we study charge-conserving many-body topological phases of fermions protected respectively by…
We discuss a cluster-like 1D system with triplet interaction. We study the topological properties of this system. We find that the degeneracy depends on the topology of the system, and well protected against external local perturbations.…
In this work, we present a theory for topological phases for quantum systems on tree graphs. Conventionally, topological phases of matter have been studied in regular lattices, but also in quasicrystals and amorphous settings. We consider…
The interest in the topological properties of materials brings into question the problem of topological phase transitions. As a control parameter is varied, one may drive a system through phases with different topological properties. What…
It is well-known that in two dimensions Turing systems produce spots, stripes and labyrinthine patterns, and in three dimensions lamellar and spherical structures or their combinations are observed. We study transitions between these states…
Topological characteristics reveal important physical properties of plasma structures and astrophysical processes. Physical parameters and constraints are linked with topological invariants, which are important for describing magnetic…
Topological insulators are insulating in the bulk but feature conducting states on their surfaces. Standard methods for probing their topological properties largely involve probing the surface, even though topological invariants are defined…
Topology is key in describing unconventional quantum phases of matter and devising robust quantum technology. Exactly how topology mixes with quantum mechanics remains largely unclear, as testified by the lack of a unifying microscopic…
In the 1950s Morse defined the analogue of Morse functions for topological manifolds. In many instances, when mathematicians are using techniques on topological manifolds that appear to be Morse-theoretic in nature, there is a topological…