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Register a new userTopological spin liquids in the ruby lattice with anisotropic Kitaev interactions
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The ruby lattice is a four-valent lattice interpolating between honeycomb and triangular lattices. In this work we investigate the topological spin-liquid phases of a spin Hamiltonian with Kitaev interactions on the ruby lattice using exact diagonalization and perturbative methods. The latter interactions combined with the structure of the lattice yield a model with $mathbb{Z}_2 times mathbb{Z}_2$ gauge symmetry. We mapped out the phase digram of the model and found gapped and gapless spin-liquid phases. While the low energy sector of the gapped phase corresponds to the well-known topological color code model on a honeycomb lattice, the low-energy sector of the gapless phases is described by an effective spin model with three-body interactions on a triangular lattice. A gap is opened in the spectrum in a small magnetic field. We argue that the latter phases could be possibly described by exotic excitations, whose their spectrum is richer than the Ising phase of the Kitaev model.
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We construct a short-range resonating valence-bond state (RVB) on the ruby lattice, using projected entangled-pair states (PEPS) with bond dimension $D=3$. By introducing non-local moves to the dimer patterns on the torus, we distinguish four distinct sectors in the space of dimer coverings, which is a signature of the topological nature of the RVB wave function. Furthermore, by calculating the reduced density matrix of a bipartition of the RVB state on an infinite cylinder and exploring its entanglement entropy, we confirm the topological nature of the RVB wave function by obtaining non-zero topological contribution, $gamma=-rm{ln} 2$, consistent with that of a $mathbb{Z}_2$ topological quantum spin liquid. We also calculate the ground-state energy of the spin-$frac{1}{2}$ antiferromagnetic Heisenberg model on the ruby lattice and compare it with the RVB energy. Finally, we construct a quantum-dimer model for the ruby lattice and discuss it as a possible parent Hamiltonian for the RVB wave function.
We theoretically study an exactly solvable Gamma matrix generalization of the Kitaev spin model on the ruby lattice, which is a honeycomb lattice with expanded vertices and links. We find this model displays an exceptionally rich phase diagram that includes: (i) gapless phases with stable spin fermi surfaces, (ii) gapless phases with low-energy Dirac cones and quadratic band touching points, and (iii) gapped phases with finite Chern numbers possessing the values {pm}4,{pm}3,{pm}2 and {pm}1. The model is then generalized to include Ising-like interactions that break the exact solvability of the model in a controlled manner. When these terms are dominant, they lead to a trivial Ising ordered phase which is shown to be adiabatically connected to a large coupling limit of the exactly solvable phase. In the limit when these interactions are weak, we treat them within mean-field theory and present the resulting phase diagrams. We discuss the nature of the transitions between various phases. Our results highlight the richness of possible ground states in closely related magnetic systems.
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 $mathbb{Z}_2$ 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 single-particle charge excitations are found at $mathbf{K}, mathbf{K}=(pm2pi/3, mp 2pi/3)$, with a corresponding correlation length of $xi approx 6.7$ 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
The Raman scattering with local optical excitation from the Majorana edge modes of Kitaev spin liquids and topological superconductors is studied theoretically. Although the effective one-dimensional model is common between these two cases, the coupling to the electromagnetic field is different. It is found that the Raman spectrum at low energy scales with $omega^3$ in Kitaev spin liquids while it shows the gap in topological superconductors. This is in sharp contrast to the infrared absorption, where the spectrum shows the gap in Kitaev spin liquids, while it behaves as $sim omega^2$ in topological superconductors. This indicates that the electrodynamics of Majorana edge modes depends on their higher-dimensional origins. The realistic estimate of the Raman scattering intensity is given for $alpha$-RuCl$_3$ as the candidate for Kitaev spin liquid.
We theoretically study THz-light-driven high-harmonic generation (HHG) in the spin-liquid states of the Kitaev honeycomb model with a magnetostriction coupling between spin and electric polarization. To compute the HHG spectra, we numerically solve the Lindblad equation, taking account of the dissipation effect. We find that isotropic Kitaev models possess a dynamical symmetry, which is broken by a static electric field, analogous to HHG in electron systems. We show that the HHG spectra exhibit characteristic continua of Majorana fermion excitations, and their broad peaks can be controlled by applying static electric or magnetic fields. In particular, the magnetic-field dependence of the HHG spectra drastically differs from those of usual ordered magnets. These results indicate that an intense THz laser provides a powerful tool to observe dynamic features of quantum spin liquids.
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