Excitation spectrum of spin-1 Kitaev spin liquids

Abstract

We study the excitation spectrum of the spin-1 Kitaev model using the symmetric tensor network. By evaluating the virtual order parameters defined on the virtual Hilbert space in the tensor network formalism, we confirm the ground state is in a Z2 spin liquid phase. Using the correspondence between the transfer matrix spectrum and low-lying excitations, we find that contrary to the dispersive Majorana excitation in the spin-1/2 case, the isotropic spin-1 Kitaev model has a dispersive charge anyon excitation. Bottom of the gapped singleparticle charge excitations are found at K, K = (±2π/3, ∓2π/3), with a corresponding correlation length of ξ ≈ 6.7 unit cells. The lower edge of the two-particle continuum, which is closely related to the dynamical structure factor measured in inelastic neutron scattering experiments, is obtained by extracting the excitations in the vacuum superselection sector in the anyon theory language.

Instabilities of spin-1 Kitaev spin liquid phase in presence of single-ion anisotropies

“…In future, it may be useful to study the nature of the phase transitions for D 111 anisotropy and the differences between ferromagnetic and antiferromagnetic Kitaev couplings. Density Matrix Renormalization Group (DMRG) or tensor network studies on larger system sizes may be helpful in this respect [38]. For positive sign of D 111 the two phases on either side of the transition have no broken symmetries, hence we speculate that the transition is topological in nature, although the transition could be first order.…”

“…Numerical studies have found further evidence of a gap in the excitation spectra for integer spins and for field induced spin-liquid phases [23,24,[26][27][28][29][30][31][32][33][34][35] as well as of large nearly degenerate subspaces giving rise to entropy plateaus [23,24,36,37]. In a very recent paper, Chen et al [38] have shown the existence of emergent Z 2 spin-liquid phase in the spin-one system with exotic deconfined anyonic excitations which are not Majorana fermions.…”