that topological degeneracy implies topological order (or long-range entanglement ) in the ground state. Many-body states with topological degeneracy are...

topological order occurs at zero temperature. Various topologically ordered states have interesting properties, such as (1) ground state degeneracy and...

processors, the first used a toric code with twist defects as a topological degeneracy (or topological defect) while the second used a different but related protocol...

In quantum mechanics, Kramers' theorem or Kramers' degeneracy theorem states that for every energy eigenstate of a time-reversal symmetric system with...

material. But in a topological insulator, these bands are, in an informal sense, "twisted", relative to a trivial insulator. The topological insulator cannot...

mathematical physics, a topological quantum field theory (or topological field theory or TQFT) is a quantum field theory that computes topological invariants. While...

edges. The degeneracy of a graph is the smallest value of k {\displaystyle k} for which it is k {\displaystyle k} -degenerate. The degeneracy of a graph...

tensor gauge theories. Gapped fracton models often feature a topological ground state degeneracy that grows exponentially and sub-extensively with system...

by the singular set SY of a topological space Y. Here SYn consists of all the continuous maps from the standard topological n-simplex to Y. The singular...

states (see Quantum phase transition, Quantum critical point, Topological degeneracy, Topological order) and where the overall system structure is independent...

entanglement see topological order, which is not related to the famous EPR paradox). Since short-range entangled states have only trivial topological orders we...

identifying 3+1‑dimensional topological orders. The multi-loop/string-braiding statistics of 3+1‑dimensional topological orders can be captured by the...

quantum double models. It is also the simplest example of topological order—Z2 topological order (first studied in the context of Z2 spin liquid in 1991)...

the Kitaev chain or Kitaev–Majorana chain is a simplified model for a topological superconductor. It models a one dimensional lattice featuring Majorana...

, the chromatic number equals the degeneracy plus one. For these graphs, the greedy algorithm with the degeneracy ordering is always optimal. Every β...

no degeneracy at all, low, intermediate, or high degeneracy. For example, the number of molecule atoms and the molecular weights are high degeneracy descriptors...

topologically nontrivial phase of matter, together with Helium-3 A superfluid phase, that broadens the topological classification beyond topological insulators...

inherent topological supersymmetry (TS) enabling the generalization of certain concepts from deterministic to stochastic models. Using tools of topological field...

A graph H is called a topological minor of a graph G if a subdivision of H is isomorphic to a subgraph of G. Every topological minor is also a minor....

numbers | n ⟩ {\displaystyle |n\rangle } are referred to as topological vacua. Topological vacua are not candidate vacuum states of Yang–Mills theories...

morphisms of C. The geometric realization of this simplicial set is a topological space, called the classifying space of the category C. These closely...

polygon do not consider the digon to be a proper polygon because of its degeneracy in the Euclidean case. A digon as a face of a polyhedron is degenerate...

Topological censorship Topological conjugacy Topological defect Topological degeneracy Topological entropy Topological entropy in physics Topological...

vertices. embedding A graph embedding is a topological representation of a graph as a subset of a topological space with each vertex represented as a point...

the geometric and topological information belonging to a 3-manifold. Thus, there is an interplay between group theory and topological methods. 3-manifolds...

corresponding topological phase transitions. Topological phases are quantum phases of matter that are characterized by robust ground state degeneracy and quantized...

one-form, and the non-integrability condition translates into a maximal non-degeneracy condition on the form. These conditions are opposite to two equivalent...

Java. https://github.com/w8r/GreinerHormann An implementation in JavaScript JTS Topological Suite A topological suite with a Java implementation v t e...

notions form the basis of topological definitions of polyhedra, as subdivisions of a topological manifold into topological disks (the faces) whose pairwise...

(2015), "Topological Insulators, Topological Dirac semimetals, Topological Crystalline Insulators, and Topological Kondo Insulators", Topological Insulators...