Fibonacci Topological Superconductor

Abstract

We introduce a model of interacting Majorana fermions that describes a superconducting phase with a topological order characterized by the Fibonacci topological field theory. Our theory, which is based on a $SO(7{)}_1/(G_2{)}_1$ coset factorization, leads to a solvable one dimensional model that is extended to two dimensions using a network construction. In addition to providing a description of the Fibonacci phase without parafermions, our theory predicts a closely related "anti-Fibonacci" phase, whose topological order is characterized by the tricritical Ising model. We show that Majorana fermions can split into a pair of Fibonacci anyons, and propose an interferometer that generalizes the $Z_2$ Majorana interferometer and directly probes the Fibonacci non-Abelian statistics.

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Cited by in corpus (32)

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• Anyons in Multichannel Kondo Systems
• Interacting Majorana Fermions
• Kondo-based Qubits for Topological Quantum Computation
• Topological holography, quantum criticality, and boundary states
• Microscopic Study of the Halperin - Laughlin Interface through Matrix Product States
• Model States for a Class of Chiral Topological Order Interfaces
• Coupled wire construction of a topological phase with chiral tricritical Ising edge modes
• A non-Abelian twist to integer quantum Hall states
• Engineering Yang-Lee anyons via Majorana bound states
• Universal topological quantum computation with strongly correlated Majorana edge modes
• Ferroelectric topological superconductor
• Non-Abelian Anyons and Non-Abelian Vortices in Topological Superconductors
• Chiral Sachdev-Ye model: Integrability and chaos of anyons in 1+1d
• Quantum simulation of the tricritical Ising model in tunable Josephson junction ladders
• Odd-frequency pairing in a superconductor coupled to two parallel nanowires
• Superconducting correlations out of repulsive interactions on a fractional quantum Hall edge
• A composite particle construction of the Fibonacci fractional quantum Hall state
• Chiral topologically ordered insulating phases in arrays of interacting integer quantum Hall islands
• Symmetry-protected topological phases, conformal criticalities, and duality in exactly solvable SO($n$) spin chains
• Dihedral twist liquid models from emergent Majorana fermions
• Exact solution of a quantum integrable system associated with the $G_2$ exceptional Lie algebra
• Disorder-induced topological superconductivity in a spherical quantum-Hall--superconductor hybrid
• Majorana zero modes in a quantum wire platform without Rashba spin-orbit coupling
• $G_2$ Integrable Point Characterization via Isotropic Spin-3 Chains
• Dissipationless topological quantum computation for Majorana objects in sparse-dense mixed encoding process
• Fibonacci topological phase in arrays of anyonic chains
• Edge optical effect as a probe of chiral topological superconductors
• Chiral Edge States Emerging on Anyon-Net
• From $G_2$ to $SO(8)$: Emergence and reminiscence of supersymmetry and triality
• Repulsive-Interaction-Driven Topological Superconductivity in a Landau Level Coupled to an $s$-Wave Superconductor
• Revealing Superconducting Chiral Edge Modes via Resistance Distributions