Nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field

Abstract

We investigate the nonlinear response of the Kitaev honeycomb lattice model in a weak magnetic field using the theory of two-dimensional coherent spectroscopy. We observe that at the isotropic point in the non-Abelian phase of this model, the nonlinear spectrum in the 2D frequency domain consists of sharp signals that originate from the flux excitations and Majorana bound states. Signatures of different flux excitations can be clearly observed in this spectrum, such that one can observe evidences of flux states with 4-adjacent, 2-non-adjacent, and 4-far-separated fluxes, which are not visible in linear response spectroscopy such as neutron scattering experiments. Moreover, in the Abelian phase we perceive that the spectrum in the frequency domain is composed of streak signals. These signals, as in the nonlinear response of the pure Kitaev model, represent a distinct signature of itinerant Majorana fermions. However, deep in the Abelian phase whenever a Kitaev exchange coupling is much stronger than the others, the streak signals are weakened and only single sharp spots are seen in the response, which resembles the dispersionless response of the conventional toric code.

15 pages, 9 figures

References in corpus (20)

• Non-Abelian Anyons and Topological Quantum Computation
• Mott Insulators in the Strong Spin-Orbit Coupling Limit: From Heisenberg to a Quantum Compass and Kitaev Models
• $\alpha$-RuCl3: a Spin-Orbit Assisted Mott Insulator on a Honeycomb Lattice
• Models and Materials for Generalized Kitaev Magnetism
• Scattering Continuum and Possible Fractionalized Excitations in $\alpha$-RuCl${}_3$
• Exact results for spin dynamics and fractionization in the Kitaev Model
• Vaporization of Kitaev spin liquids
• Magnetic Excitations and Continuum of a Field-Induced Quantum Spin Liquid in $\alpha$-RuCl${}_3$
• Raman Scattering Signatures of Kitaev Spin Liquids in A${}_2$ IrO${}_3$ Iridates
• Raman spectroscopic signature of fractionalized excitations in the harmonic-honeycomb iridates $\beta$- and $\gamma$-Li${}_2$IrO${}_3$
• Kitaev Materials
• Physical states and finite-size effects in Kitaev's honeycomb model: Bond disorder, spin excitations, and NMR lineshape
• A Description of Kitaev's Honeycomb Model with Toric-Code Stabilizers
• Towards Kitaev Spin Liquid in 3d Transition Metal Compounds
• Photon echo from lensing of fractional excitations in Tomonaga-Luttinger spin liquid
• Nonlinear spectroscopy of bound states in perturbed Ising spin chains
• Emergence of string-valence bond solid state in the frustrated $J_1-J_2$ transverse field Ising model on the square lattice
• Magnon-spinon dichotomy in the Kitaev hyperhoneycomb $\beta$-Li${}_2$IrO${}_3$
• Quantum phase diagram of two-dimensional transverse field Ising model: unconstrained tree tensor network and mapping analysis
• Signatures of non-Loudon-Fleury Raman scattering in the Kitaev magnet $\beta$-Li${}_2$IrO${}_3$

Cited by in corpus (7)

• Exploring Two-dimensional Coherent Spectroscopy with Exact Diagonalization: Spinons and Confinement in 1D Quantum Magnets
• Photon echo and fractional excitation lensing of $S=1/2$ XY spin chain
• Revealing Quadrupolar Excitations with Non-Linear Spectroscopy
• Two-dimensional coherent spectrum of high-spin models via a quantum computing approach
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• Diagnosing electronic phases of matter using photonic correlation functions
• The Kekulé-Kitaev model: linear and non-linear responses and magnetic field effects