Abstract
This paper unifies the Teo-Kane theory of a point-contact in the quantum spin Hall effect and the Affleck-Giuliano theory of a junction between a topological superconductor and two quantum wires. The authors show that the two problems are related by duality
Highlights
Quantum impurity problems have played a central role in the development of quantum many-body theory
Applying the powerful techniques of boundary conformal field theory [3] allows for a detailed characterization of non-Fermi-liquid behavior that arises in the multichannel Kondo problem [1,2], the single-impurity problem in a Luttinger liquid [4,5,6], the theory of point contacts in the fractional quantum Hall effect [7,8], and many related problems
We show that the helical point contact described by the Teo and Kane [14] (TK) model and the Luttinger liquid–topological superconductor junction described by the AG model are equivalent and related by a duality transformation
Summary
Quantum impurity problems have played a central role in the development of quantum many-body theory. A central paradigm, introduced by Affleck and Ludwig [1,2], is that the fixed points characterizing the low-energy phases of a (0 + 1)dimensional impurity coupled to a bath are in correspondence with the allowed conformally invariant boundary conditions of the conformal field theory describing the bath. Spin Hall insulator, which forms a nonchiral Luttinger liquid [12,13] This led Teo and Kane [14] (TK) to develop a theory of the critical behavior of the pinch-off transition of a helical point contact. For the helical point contact, both the pinchedoff and the open limits (which both correspond to simple conformally invariant boundary conditions) are perturbatively stable when 1/2 < K < 2 In both cases, the perturbative corrections involve tunneling of electrons between the middles of two Luttinger liquids, which is irrelevant for any K = 1.
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