相互作用任意子链中的平移不变性、拓扑和临界性保护
Translation invariance, topology, and protection of criticality in chains of interacting anyons
摘要：
利用有限尺寸标度变元，可以从有限系统的低能谱中提取相互作用任意子链的临界性质。In Phys. Rev. Lett. 98，160409（2007），Feiguin等人表明，环面上的Fibonacci任意子的反铁磁（AFM）链与三临界伊辛模型处于相同的普适类，并且临界性受到拓扑对称性的保护。在本文中，我们首先回顾了图形形式主义的研究的任意子的光盘，并展示了如何这种形式主义可能会一直延伸到研究系统的表面上的更高的属。然后，我们采用这种图形形式主义研究有限环的相互作用的任意子在光盘和环面，并表明，分析光盘上必然产生的能量谱，这是一个子集，这是获得的环面。对于临界哈密顿量，可以从这个子集中提取出与系统的拓扑对称性有关的局部标度算子的标度维数。相关的考虑也适用于开链。
英文摘要：
Using finite size scaling arguments, the critical properties of a chain of interacting anyons can be extracted from the low energy spectrum of a finite system. In Phys. Rev. Lett. 98, 160409 (2007), Feiguin et al. showed that an antiferromagnetic (AFM) chain of Fibonacci anyons on a torus is in the same universality class as the tricritical Ising model, and that criticality is protected by a topological symmetry. In the present paper we first review the graphical formalism for the study of anyons on the disc and demonstrate how this formalism may be consistently extended to the study of systems on surfaces of higher genus. We then employ this graphical formalism to study finite rings of interacting anyons on both the disc and the torus, and show that analysis on the disc necessarily yields an energy spectrum which is a subset of that which is obtained on the torus. For a critical Hamiltonian, one may extract from this subset the scaling dimensions of the local scaling operators which respect the topological symmetry of the system. Related considerations are also shown to apply for open chains.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
