Introduction to Topological Quantum Matter & Quantum Computation

In the citing paper

“However, the weaklyinteracting integer quantum Hall effect (section 2.2.1) states lack the nontrivial excitations, but do possess LRE according to the above definition [6].”

In the citing paper

“However, it is now known that classification based on symmetry is not complete, since some zero-temperature phases of matter that share the same symmetries are nevertheless separated by a phase transition [6].”

In the citing paper

“A variety of interesting phenomena, like topological degeneracy of the ground state (i.e. a degeneracy robust against local perturbations that do not affect the topology of the state), exotic excitations, and robust, perfectly conducting edge states may arise due to the topological nature of these states [6].”

In the citing paper

“The topologically ordered states may have features such as topologically protected gapless boundary modes, topologically degenerate ground states and exotic excitations obeying fractional Abelian or non-Abelian statistics [6] (see section 2.2.3).”

In the citing paper

“In contrast to the gauge invariant Abelian Berry holonomy, the non-Abelian holonomy transforms as U n C → U -1 ( R 0 ) U n C U ( R 0 ) [6].”

In the citing paper

“Cyclic transport as discussed above can lead to non-Abelian geometric phases when the system is prepared in a degenerate state [7,6].”

In the citing paper

“Additionally, an explicit time dependence of the Hamiltonian may be thought of as introducing a geometric scalar potential in addition to the time-dependent vector potential A n ( k , t ) [6].”

In the citing paper

“Arectangle with periodic boundary conditions in both directions is topologically equivalent (homeomorphic) to a torus, since there are two distinct possible classes of nontrivial loops that cannot be contracted into a point without breaking them open (see [6] for a more rigorous treatment).”

In the citing paper

“SPT phases lack the topological degeneracy and nontrivial excitations, but they possess the topologically protected boundary states [6].”

In the citing paper

“On the other hand, they need not be gapless in the interacting case, provided the boundary either spontaneously breaks a symmetry that enables the existence of the SPT phase in question (in 2D or higher dimensions), or that it carries an intrinsic topological order (in 3D or higher dimensions) [6].”

In the citing paper

“with the phase shifts R 1 σσ = e -πi/ 8 , R ψ σσ = e 3 πi/ 8 [6].”

In the citing paper

“TIs are the noninteracting insulating phases topologically distinct from the trivial insulator [6].”

In the citing paper

“Berryjeva konekcija A n ( k ) = i 〈 u n k | ∇ k u n k 〉 se u 3D rešeci ponaša kao magnetski vektorski potencijal u k -prostoru [6].”

In the citing paper

“No s druge strane, podržavaju netrivijalna topološka graniˇ cna stanja [6].”

In the citing paper

“LRE faze obiˇ cno imaju egzotiˇ cna pobu ¯ denja s frakcijskom statistikom [6].”