Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model

Abstract

The one-dimensional $p$-wave superconductor, characterized by boundary Majorana modes, has attracted significant interest owing to its potential application in topological quantum computation. Similarly, spin-1/2 Kitaev ladder systems with bond-dependent Ising interactions, featuring Majorana fermions coupled with $Z_2$ flux, exhibit boundary Majorana modes when in a topological phase. However, the ground state degeneracy, inherent in these systems, may result in the annihilation of Majorana modes due to the superposition of the degenerate states. To avoid this issue, here we introduce a projective measurement that selects one of the degenerate $Z_2$ sectors, enabling the revival of Majorana modes. Once the state is selected, we show that the application of the local spin operators on a bond flips the sign of the adjacent $Z_2$ flux. Repeating such operators enables the system to reach a desired $Z_2$ flux configuration. The Majorana zero modes can be manipulated and fused by tuning the flux sectors achievable through applying local spin operators. We also discuss the engineering of the Kitaev ladder and open questions for future studies.

12 pages, 10 figures

References in corpus (19)

• Non-Abelian Anyons and Topological Quantum Computation
• Superconducting proximity effect and Majorana fermions at the surface of a topological insulator
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Introduction to topological superconductivity and Majorana fermions
• Models and Materials for Generalized Kitaev Magnetism
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Beyond Kitaev physics in strong spin-orbit coupled magnets
• Ground state and low-energy excitations of the Kitaev-Heisenberg ladder
• Majorana states in inhomogeneous spin ladders
• Reflection Positivity for Parafermions
• Phase diagrams of spin-$S$ Kitaev ladders
• Spin- and Flux-gap Renormalization in the Random Kitaev Spin Ladder
• Twice Hidden String Order and Competing Phases in the Spin-1/2 Kitaev-Gamma Ladder
• Quantum phase transition as an interplay of Kitaev and Ising interactions
• Exact weak bosonic zero modes in a spin/fermion chain
• Probing the non-Abelian fusion of a pair of Majorana zero modes

Cited by in corpus (1)

• Real-time control of non-Abelian anyons in Kitaev spin liquid under energy dissipation