论文标题
在二维中的偶性编织统计统计的有效现场理论
Effective Field Theory of Dipolar Braiding Statistics in Two Dimensions
论文作者
论文摘要
在两个维度上的哈密顿群岛的排名-2倍态代码（R2TC）可以构建为rank-2 u（1）晶格量规理论的希格斯后代。正如作者最近指出的那样[Y.-T。哦，J。Kim，E.-G。 Moon和J. H. Han，物理。 Rev. b {\ bf 105}，045128]该模型中的准粒子显示出异常的编织统计量，这取决于参与编织的粒子的初始位置。我们表明，这种新型的统计阶段捕获了编织中包含的准粒子的总偶极力矩，与传统的ven nyonic编织形成鲜明对比的是总电荷。对这种{\ IT偶性编织统计}的Aharonov-bohm解释是根据源自基础的Rank-2仪表字段构建的紧急级别1向量电位的。开发了R2TC中准粒子动力学的相关场理论，并得出了随附的保护定律。与捕获rank-1八极分子的BF理论相比，构建了等级-2量规场的{\ IT偶性BF理论}，并显示出可以正确捕获偶性编织统计的统计。
A rank-2 toric code (R2TC) Hamiltonian in two dimensions can be constructed as a Higgsed descendant of rank-2 U(1) lattice gauge theory. As noted by the authors recently, [Y.-T. Oh, J. Kim, E.-G. Moon, and J. H. Han, Phys. Rev. B {\bf 105}, 045128] the quasiparticles in that model shows unusual braiding statistics that depends on the initial locations of the particles which participate in the braiding. We show that this new kind of statistical phase captures the total dipole moment of quasiparticles encompassed in the braiding, in contrast to the conventional anyonic braiding seeing the total charge. An Aharonov-Bohm interpretation of such {\it dipolar braiding statistics} is made in terms of emergent, rank-1 vector potentials that are built out of the underlying rank-2 gauge fields. Pertinent field theories of the quasiparticle dynamics in the R2TC are developed, and the accompanying conservation laws derived. A {\it dipolar BF theory} of the rank-2 gauge fields is constructed and shown to correctly capture the dipolar braiding statistics, in contrast to the conventional BF theory capturing the monopolar braiding statistics of anyons in the rank-1 toric code.
