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Z(3) Quantum Double in a Superconducting Wire Array

TitleZ(3) Quantum Double in a Superconducting Wire Array
Publication TypeJournal Article
Year of Publication2021
AuthorsZ-C. Yang, D. Green, H. Yu, and C. Chamon
JournalPRX Quantum
Volume2
Date PublishedAUG 13
Type of ArticleArticle
Abstract

We show that a Z(3) quantum double can be realized in an array of superconducting wires coupled via Josephson junctions. With a suitably chosen magnetic flux threading the system, the interwire Josephson couplings take the form of a complex Hadamard matrix, which possesses combinatorial gauge symmetry-a local Z(3) symmetry involving permutations and shifts by +/- 2 pi/3 of the superconducting phases. The sign of the star potential resulting from the Josephson energy is inverted in this physical realization, leading to a massive degeneracy in the nonzero flux sectors. A dimerization pattern encoded in the capacitances of the array lifts up these degeneracies, resulting in a Z(3) topologically ordered state. Moreover, this dimerization pattern leads to a larger effective vison gap as compared to the canonical case with the usual (uninverted) star term. We further show that our model maps to a quantum three-state Potts model under a duality transformation. We argue, using a combination of bosonization and mean field theory, that altering the dimerization pattern of the capacitances leads to a transition from the Z(3) topological phase into a quantum XY-ordered phase. Our work highlights that combinatorial gauge symmetry can serve as a design principle to build quantum double models using systems with realistic interactions.

DOI10.1103/PRXQuantum.2.030327