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Bulletin of the American Physical Society

The realization of Majorana fermions in Kitaev Quantum Spin Lattice

Seung-Hwan Do, Sang‐Youn Park, Junki Yoshitake, Joji Nasu, Yukitoshi Motome, Younghak Kwon, Devashibhai Thakarshibhai Adroja, David J. Voneshen, J.-H. Park, Kwang‐Yong Choi, Sungdae Ji

Published Mar 13, 2017• 0 citations
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Abstract We study magnetic Raman, i.e. inelastic light, scattering of Kitaev’s quantum spin liquids realizable in honeycomb nanoribbons. Elementary excitations in the Kitaev spin liquids consist of itinerant Majorana (matter) fermions and localized gauge fluxes (visons). Matter fermions are characterized by the projective point (gauged rotation) group inherent in the lattice. Inelastic light scattering is mediated by a pair of matter fermions without any vison excitation. We can selectively “observe” matter fermions of the same symmetry and those of different symmetries depending on the polarization of incoming and/or outgoing lights. A pair of matter fermions with particular translational quantum numbers ±k cannot be Raman active.
The Sachdev-Ye-Kitaev (SYK) model is zero-dimensional model simulating quantum chaos using interacting Majorana fermions.Previously proposals have been made to realize the SYK model in fermionic systems that can support majorana zero modes. In this work, we simulate the SYK model in a Kitaev spin chain, where zero modes also exist in the ground state from the fermionic representation of spins. By adding other interactions as perturbations, we lift the degenerate majorana zero modes and obatin an effective SYK interactions. Although the majorana fermions are nonlocal in forms of spin operators, we show that the out-of-time-ordered correlator (OTOC) of the majorana fermions can be approximately simulated in forms of spin operators. Our proposal sheds light in simulating the fermonic SKY model and the related physics in purely bosonic systems.
The Kitaev honeycomb model (KHM) consists of spin-1/21/21/2 particles on a honeycomb lattice with direction-dependent Ising-like interactions. It can alternatively be described in terms of non-interacting Majorana fermions, can be solved exactly, and has a quantum spin-liquid ground state. Open boundaries then host Majorana zero modes (MZMs) that are robust against some types of disorder. We analyze the fate of the MZMs when they couple to an environment via a Lindblad master equation. By computing the time evolution of the density matrix, we find that when decoherence occurs, the steady state is mostly the maximally mixed state. Among the few exceptions is a parameter regime that realizes the superconducting Kitaev chain model with periodic boundary conditions. We consistently observe a quantum Zeno effect in the density matrix as well as in the entropy and fidelity, while it is not found in the energy gap of some gapped spin liquids. We thus present a comprehensive overview over MZMs coupled to a spin bath that is relevant to proposals to detect MZMs of Kitaev layers on surfaces using scanning tunneling microscopy (STM).