Dynamical structure factor in the non-Abelian phase of the Kitaev honeycomb model in the presence of quenched disorder

Abstract

Kitaev's model of spins interacting on a honeycomb lattice describes a quantum spin-liquid, where an emergent static Z2 gauge field is coupled to Majorana fermions. In the presence of an external magnetic field and for a range of interaction strengths, the system behaves as a gapped, non-Abelian quantum spin-liquid. In this phase, the vortex excitations of the emergent Z2 gauge field have Majorana zero modes bound to them. Motivated by recent experimental progress in measuring and characterizing real materials that could exhibit spin-liquid behavior, we analytically calculate the dynamical spin structure factor in the non-Abelian phase of the Kitaev's honeycomb model. In particular, we treat the case of quenched disorder in the vortex configurations. Our calculations reveal a peak in the low-energy dynamical structure factor that is a signature of the spin-liquid behavior. We map the effective Hamiltonian to that of a chiral p-wave superconductor by using the Jordan-Wigner transformation. Subsequently, we analytically calculate the wave functions of the Majorana zero modes, the energy splitting for finite separation of the vortices and finally, the dynamical structure factor in presence of quenched disorder.

Geometric description of the Kitaev honeycomb lattice model

“…In this paper, we investigate geometric description of the Kitaev honeycomb lattice model (KHLM) 35 , the well-known two-dimensional (2D) model of interacting spin-1 2 particles that gives rise to a quantum spin liquid phase with topological order. A salient feature of the KHLM is that it can support non-Abelian anyons in the form of Majorana zero modes (MZMs) trapped at its vortices [35][36][37][38][39] . Similar to the FQH effect 40 , the KHLM is both topologically ordered in the sense that it can support anyonic excitations and it is a topological phase categorised by a non-trivial Chern number 35,41 .…”

Equivalence between vortices, twists, and chiral gauge fields in the Kitaev honeycomb lattice model

“…The main interest in the KHLM is that vortices imprinted in the system trap localised Majorana zero modes that behave as non-Abelian anyons 4,[6][7][8][9][10][11][12][13][14][15][16] . This property, together with the possibility of realising this model in the laboratory with crystallised materials [17][18][19][20] , makes KHLM of interest to anyonic quantum computation 6,21,22 as well as to the investigation of fundamental physics of materials that support non-Abelian anyons.…”

Magnetoelectric generation of a Majorana-Fermi surface in Kitaev's honeycomb model

“…Specifically, in transition metal magnets with strong spin-orbit coupling, a microscopic superexchange mechanism has been identified for an edge-shared bonding geometry [9] that yields Kitaev's anisotropic exchange interaction at leading order [10][11][12]. As such, Kitaev's model has been the subject of intense study [13] to determine its response to a variety of perturbations and probes, including mapping the nearby phase diagram [10][11][12][14][15][16] with an eye towards materials, understanding thermal properties [17][18][19][20], computing its dynamical responses [21][22][23][24][25][26], generalizing it to three-dimensional lattices [27][28][29][30][31][32][33], as well as understanding the effects of disorder [34][35][36][37][38][39].…”