Vortex Loops and Majoranas

Abstract

We investigate the role that vortex loops play in characterizing eigenstates of interacting Majoranas. We first give some general results, and then we focus on ladder Hamiltonian examples to test further ideas. Two methods yield exact results: i.) We utilize the mapping of spin Hamiltonians to quartic interactions of Majoranas and show under certain conditions the spectra of these two examples coincide. ii) In cases with reflection-symmetric Hamiltonians, we use reflection positivity for Majoranas to characterize vortices. Aside from these exact results, two additional methods suggest wider applicability of these results: iii.) Numerical evidence suggests similar behavior for certain systems without reflection symmetry. iv.) A perturbative analysis also suggests similar behavior without the assumption of reflection symmetry.

28 pages

References in corpus (9)

• Schrieffer-Wolff transformation for quantum many-body systems
• Topological characterization of quantum phase transitions in a S=1/2 spin model
• Exact results on the Kitaev model on a hexagonal lattice: spin states, string and brane correlators, and anyonic excitations
• Topological phases, Majorana modes and quench dynamics in a spin ladder system
• Physical solutions of the Kitaev honeycomb model
• Majorana states in inhomogeneous spin ladders
• Symmetry Protected Topological Phases in Spin Ladders with Two-body Interactions
• Manipulating unpaired Majorana fermions in a quantum spin chain
• Majorana Spin Liquids on a two-leg ladder

Cited by in corpus (9)

• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Theory of Raman response in three-dimensional Kitaev spin liquids: application to $\beta -$ and $\gamma -$Li${}_2$IrO${}_3$ compounds
• Reflection Positivity for Parafermions
• Non-Abelian chiral spin liquid on a simple non-Archimedean lattice
• Reflection Positivity for Majoranas
• Cluster state generation in one-dimensional Kitaev honeycomb model via shortcut to adiabaticity
• Hyperbolic Spin Liquids
• Quasicrystalline Spin Liquid
• Reviving Majorana zero modes in the spin-1/2 Kitaev ladder model