Coexistence of Strong and Weak Majorana Zero Modes in Anisotropic XY Spin Chain with Second-Neighbor Interaction

Abstract

We theoretically investigate Majorana zero modes emerging in an anisotropic XY spin chain with second neighbor interactions. The spin chain is mathematically equivalent to the Kitaev chain composing of spinless fermions if only nearest-neighbor interactions are considered. Recent studies on the Kitaev chain with long-ranged interactions, have presented coexistence of several Majorana zero modes. Investigating the topological phase diagram of the anisotropic XY spin chain with second neighbor interactions, we find coexistence of several Majorana zero modes similar to the Kitaev chain. However, we confirm that one of zero modes is restricted into a Hilbert subspace. The mode is regarded as a so-called weak zero mode that should exhibit thermodynamical properties different from a (strong) zero mode appearing in the whole Hilbert space. Since the quantum statistics of spin is the same as a hard-core boson, we expect an experimental realization of the weak mode in not only quantum spin materials but also optical lattices for cold atom systems.

13 pages, 7 figures

References in corpus (30)

• Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices
• The density-matrix renormalization group in the age of matrix product states
• Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures
• Classification of topological insulators and superconductors in three spatial dimensions
• Evidence of Majorana fermions in an Al - InAs nanowire topological superconductor
• Observation of Majorana Fermions in Ferromagnetic Atomic Chains on a Superconductor
• Observation of Majorana Fermions in a Nb-InSb Nanowire-Nb Hybrid Quantum Device
• Colloquium: Majorana Fermions in nuclear, particle and solid-state physics
• Anomalous modulation of a zero bias peak in a hybrid nanowire-superconductor device
• Majorana qubit decoherence by quasiparticle poisoning
• Observation of a Majorana zero mode in a topologically protected edge channel
• Fermion Fractionalization to Majorana Fermions in Dimerized Kitaev Superconductor
• Stability of Majorana Fermions in Proximity-Coupled Topological Insulator Nanowires
• Stability of zero modes in parafermion chains
• Decoherence of Majorana qubits by noisy gates
• Majorana fermions in density modulated p-wave superconducting wires
• Dynamics of almost strong edge modes in spin chains away from integrability
• Majorana Kramers pairs in Rashba double nanowires with interactions and disorder
• Robustness of Majorana edge modes and topological order -- exact results for the symmetric interacting Kitaev chain with disorder
• Characterization of topological phases of modified dimerized Kitaev chain via edge correlation functions
• Exact solution to an interacting dimerized Kitaev model at symmetric point
• Exact solutions and topological phase diagram in interacting dimerized Kitaev topological superconductors
• Study of the phase diagram of the Kitaev-Hubbard chain
• Majorana Zero-Energy Mode and Fractal Structure in Fibonacci-Kitaev Chain
• Influence of long-range interaction on Majorana zero modes
• Majorana phase-gate based on the geometric phase
• Phase diagram and topological order in the modulated $XYZ$ chain with magnetic fields
• Reentrant Topological Phase Transition in a Bridging Model between Kitaev and Haldane Chains
• Polynomial description of inhomogeneous topological superconducting wires
• A Study of Topological Quantum Phase Transition and Majorana Localization Length for the Interacting Helical Liquid System

Cited by in corpus (7)

• Topological and quantum critical properties of the interacting Majorana chain model
• Dephasing enhanced strong Majorana zero modes in 2D and 3D higher-order topological superconductors
• Exact weak bosonic zero modes in a spin/fermion chain
• Critical region of topological trivial and nontrivial phases in interacting Kitaev chain with spatially varying potentials
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model
• Quantifying robustness and locality of Majorana bound states in interacting systems
• Strong and almost strong modes of Floquet spin chains in Krylov subspaces