Spin Transport in the Quantum Spin Liquid State in the S = 1 Kitaev Model: Role of the Fractionalized Quasiparticles

Abstract

We investigate the real-time spin response of the S = 1 Kitaev model upon stimuli of a pulsed magnetic field in the one of the edges using the exact diagonalization method. It is found that the pulsed magnetic field has no effect on the appearance of the spin moments in the quantum spin liquid region, but induces the spin oscillations in the other edge region with a small magnetic field. This is understood by the existence of the itinerant quasiparticles, which carries the spin excitations without the spin polarization in the quantum spin liquid state. This suggests that the spin fractionalizations occur in the S = 1 Kitaev model as well as the exactly solvable S = 1/2 Kitaev one and the fractionalized quasiparticles play an essential role in the spin transport.The Kitaev model has attracted much interest since the proposal of the quantum spin model by A. Kitaev 1) and suggestion of its implementation in real materials. 2) This model is composed of direction-dependent Ising exchange interactions on a honeycomb lattice, which is exactly solvable and its ground state is a quantum spin liquid (QSL) with short-range spin correlations. In this model, quantum spins are fractionalized into the localized and itinerant Majorana fermions due to the quantum many-body effect. 1, 3-5) The Majorana fermions have been observed recently as a half-quantized plateau in the thermal quantum Hall experiments in the candidate material α-RuCl 3 . 6-10) Furthermore, it is theoretically clarified that distinct energy scales ascribed to the fractionalization appear in the thermodynamic properties such as a double-peak structure in the specific heat, 11,12) which stimulates further theoretical and experimental investigations on the spin fractionalization. [13][14][15][16][17][18] Recently, the generalization of the Kitaev model with arbitrary spins 19) has been studied, [20][21][22][23][24][25][26][27][28][29] where similar double peaks in the specific heat have been reported. 21) Therefore, the spin fractionalizations are naively expected even in the spin-S Kitaev model although it is no longer solvable.In our previous manuscipt, 30) we have studied the real-time dynamics of the S = 1/2 Kitaev model by means of the Majorana mean-field theory. It has been found that, even in the Kitaev QSL with extremely short-ranged spin correlations, the spin excitation propagates in the bulk without spin polarization. This suggests that the spin transport is not caused by the change of local magnetization, but is mediated by the itinerant Majorana fermions. Therefore, the real-time simulation for the spin transport is one of the promising approaches to examine the existence of the itinerant quasiparticles in the spin-S Kitaev model.In this paper, we investigate the real-time dynamics of the S = 1 Kitaev model on the honeycomb lattice with two edges by means of the exact diagonalization method. We demonstrate that after the pulsed magnetic field is applied to one of the edges, the oscillation of spin moments does not appear in the bulk, but is induced in...

Thermally enhanced Majorana-mediated spin transport in the Kitaev model

“…To clarify how the Majorana-mediated spin transport is modified at finite temperatures, we first focus on the time evolution of the nearest-neighbor spin-spin correlations C µ ij (t) on the µ-bond. This quantity is proportional to the bond energy, and thereby the oscillation indicates the energy flow for the Majorana-mediated transport [14]. Figure 4 shows the real-time evolution of the change in the spin-spin correlations in the M region.…”

“…We note that in the regions under the finite magnetic field, the local operator W p is no longer a conserved quantity. For example, the local operator on the pla-quette composed of the sites (5,12,13,14,7,6) shown in Fig. 1(a) does not commute with −h R S z 7 .…”

“…In both cases, the spin current flows in materials with magnetic orders. On the other hand, it has been revealed that the spin transport is also realized in quantum spin liquids (QSLs) [13][14][15], where no magnetic order is realized due to strong quantum fluctuations [16][17][18][19][20][21][22]. One of the typical examples is provided by an antiferromagnetic S = 1/2 Heisenberg chain.…”

“…The itinerant Majorana fermions have been observed as a half quantized plateau in the thermal quantum Hall experiments [25,26] in a candidate α-RuCl 3 [27]. Furthermore, it has been reported that the itinerant Majorana fermions play a crucial role for the spin transport without spin oscillations [13][14][15]. It is known that Majorana and flux excitations have distinct energy scales, which leads to interesting thermodynamic properties such as the double peaks in the specific heat and the plateau in the entropy [28,29].…”

Stabilization of a honeycomb lattice of IrO6 octahedra by formation of ilmenite-type superlattices in MnTiO3

“…Such a spin-disordered (or spin-frustrated) state may be associated with quantum spin liquids, although the experimental identification of the featureless magnetic ground state in ultrathin films presents a great challenge [43][44][45] . The next step is to understand the spin structures (including the Ir sites) and the excited-state properties in Mn−Ir−O using recently advanced diagnostics such as Raman spectroscopy 1,5,46 and in-plane spin transport measurements [47][48][49][50] . In addition, the structural quality of a sample is important for the formation of pure Kitaev materials.…”