拓扑超导相的Chern-Simons-Higgs跃迁
Chern-Simons-Higgs transitions out of Topological Superconducting Phases
摘要：
在这项研究中，我们研究了有效场论的超导相位与拓扑秩序，连接到建议实现的奇异拓扑相位（包括托管伊辛和斐波那契任意子）的超导量子霍尔异质结构。我们的非阿贝尔超导态的有效场论是非阿贝尔的Chern-Simons理论，其中涡旋-准粒子复合物的凝聚导致了相关的阿贝尔量子Hall态。这种陈-西蒙斯-希格斯凝聚过程是对偶的超导非阿贝尔拓扑相位耦合链结构的出现。在这种跃迁中，系统的手性中心荷通常会发生变化，因此它们不属于Bais和Slingerland提出的玻色子凝聚跃迁的描述范围（尽管当所描述的跃迁重合时，这两种方法是一致的）。我们的凝聚过程可以推广到基于任意李群的陈-西蒙斯理论，总是描述从李代数到它的Cartan子代数的过渡。我们包括几个有启发性的例子，这种过渡。
英文摘要：
In this study, we examine effective field theories of superconducting phases with topological order, making connection to proposed realizations of exotic topological phases(including those hosting Ising and Fibonacci anyons) in superconductor-quantum Hall heterostructures. Our effective field theories for the non-Abelian superconducting states are non-Abelian Chern-Simons theories in which the condensation of vortex-quasiparticle composites lead to the associated Abelian quantum Hall states. This Chern-Simons-Higgs condensation process is dual to the emergence of superconducting non-Abelian topological phases in coupled chain constructions. In such transitions, the chiral central charge of the system generally changes, so they fall outside the description of bosonic condensation transitions put forth by Bais and Slingerland (though the two approaches agree when the described transitions coincide). Our condensation process may be generalized to Chern-Simons theories based on arbitrary Lie groups, always describing a transition from a Lie Algebra to its Cartan subalgebra. We include several instructive examples of such transitions.
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