Anyons and transmutation of statistics via vacuum induced Berry phase

Intermediate symmetric construction of transformation between anyon and Gentile statistics

Gentile statistics describes fractional statistical systems in the occupation number representation. Anyon statistics researches those systems in the winding number representation. Both of them are intermediate statistics between Bose-Einstein and Fermi-Dirac statistics. The second quantization of Gentile statistics shows a lot of advantages. According to the symmetry requirement of the wave function, we give the general construction of transformation between anyon and Gentile statistics. In other words, we introduce the second quantization form of anyons in a easy way. Basic relations of seco…

Engineering statistical transmutation of identical quantum particles

A fundamental pillar of quantum mechanics concerns indistinguishable quantum particles. In three dimensions they may be classified into fermions or bosons, having, respectively, antisymmetric or symmetric wave functions under particle exchange. One of numerous manifestations of this quantum statistics is the tendency of fermions (bosons) to anti-bunch (bunch). In a two-particle scattering experiment with two possible outgoing channels, the probability of the two particles to arrive each at a different terminal is enhanced (with respect to classical particles) for fermions, and reduced for boso…

玻色子的任意子化

Anyonization of bosons

本文在一维强相互作用量子气体中利用移动杂质和自旋-电荷分离实现了可调统计角的任意子关联，并通过动量分布观测到玻色子向费米子的嬗变，为研究非平衡任意子现象开辟了新途径。

Exchanging identical particles and topological quantum computing

The phase factor $(-1)^{2s}$ that features in the exchange symmetry for identical spin-$s$ fermions or bosons is not simply and automatically equal to the phase factor one can observe in an interference experiment that involves physically exchanging two such particles. The observable phase contains, in general, single-particle geometric and dynamical phases as well, induced by both spin and spatial exchange transformations. By extending the analysis to (non-abelian) anyons it is argued that, similarly, there are single-anyon geometric and dynamical contributions in addition to purely topologic…

Projective non-Abelian Statistics of Dislocation Defects in a Z_N Rotor Model

Non-Abelian statistics is a phenomenon of topologically protected non-Abelian Berry phases as we exchange quasiparticle excitations. In this paper, we construct a Z_N rotor model that realizes a self-dual Z_N Abelian gauge theory. We find that lattice dislocation defects in the model produce topologically protected degeneracy. Even though dislocations are not quasiparticle excitations, they resemble non-Abelian anyons with quantum dimension sqrt(N). Exchanging dislocations can produces topologically protected projective non-Abelian Berry phases. The dislocations, as projective non-Abelian anyo…

$\mathbb{Z}_2$ 格点规范理论：费米子规范、嬗变与 Kramers-Wannier 对偶性

$\mathbb{Z}_2$ lattice gauge theories: fermionic gauging, transmutation, and Kramers-Wannier dualities

本文通过插入马约拉纳费米子推广 $\mathbb{Z}_2$ 对称性规范固定，建立玻色子与费米子格点系统的对偶对应，构造马约拉纳稳定子码，并证明与常规 $\mathbb{Z}_2$ 规范理论的酉等价性，为量子计算提供统一框架。