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Register a new userQuantum gap and spin-wave excitations in the Kitaev model on a triangular lattice
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We study the effects of quantum fluctuations on the dynamical generation of a gap and on the evolution of the spin-wave spectra of a frustrated magnet on a triangular lattice with bond-dependent Ising couplings, analog of the Kitaev honeycomb model. The quantum fluctuations lift the subextensive degeneracy of the classical ground-state manifold by a quantum order-by-disorder mechanism. Nearest-neighbor chains remain decoupled and the surviving discrete degeneracy of the ground state is protected by a hidden model symmetry. We show how the four-spin interaction, emergent from the fluctuations, generates a spin gap shifting the nodal lines of the linear spin-wave spectrum to finite energies.
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We identify and discuss the ground state of a quantum magnet on a triangular lattice with bond-dependent Ising-type spin couplings, that is, a triangular analog of the Kitaev honeycomb model. The classical ground-state manifold of the model is spanned by decoupled Ising-type chains, and its accidental degeneracy is due to the frustrated nature of the anisotropic spin couplings. We show how this subextensive degeneracy is lifted by a quantum order-by-disorder mechanism and study the quantum selection of the ground state by treating short-wavelength fluctuations within the linked cluster expansion and by using the complementary spin-wave theory. We find that quantum fluctuations couple next-nearest-neighbor chains through an emergent four-spin interaction, while nearest-neighbor chains remain decoupled. The remaining discrete degeneracy of the ground state is shown to be protected by a hidden symmetry of the model.
We consider the quasi-two-dimensional pseudo-spin-1/2 Kitaev - Heisenberg model proposed for A2IrO3 (A=Li, Na) compounds. The spin-wave excitation spectrum, the sublattice magnetization, and the transition temperatures are calculated in the random phase approximation (RPA) for four different ordered phases, observed in the parameter space of the model: antiferomagnetic, stripe, ferromagnetic, and zigzag phases. The N{e}el temperature and temperature dependence of the sublattice magnetization are compared with the experimental data on Na2IrO3.
A quantum spin liquid (QSL) is an exotic state of matter in which electrons spins are quantum entangled over long distances, but do not show symmetry-breaking magnetic order in the zero-temperature limit. The observation of QSL states is a central aim of experimental physics, because they host collective excitations that transcend our knowledge of quantum matter; however, examples in real materials are scarce. Here, we report neutron-scattering measurements on YbMgGaO4, a QSL candidate in which Yb3+ ions with effective spin-1/2 occupy a triangular lattice. Our measurements reveal a continuum of magnetic excitations - the essential experimental hallmark of a QSL - at very low temperature (0.06 K). The origin of this peculiar excitation spectrum is a crucial question, because isotropic nearest-neighbor interactions do not yield a QSL ground state on the triangular lattice. Using measurements of the magnetic excitations close to the field-polarized state, we identify antiferromagnetic next-nearest-neighbor interactions in the presence of planar anisotropy as key ingredients for QSL formation in YbMgGaO4.
We calculate the fermionic spectral function $A_k (omega)$ in the spiral spin-density-wave (SDW) state of the Hubbard model on a quasi-2D triangular lattice at small but finite temperature $T$. The spiral SDW order $Delta (T)$ develops below $T = T_N$ and has momentum ${ bf K} = (4pi/3,0)$. We pay special attention to fermions with momenta ${bf k}$, for which ${bf k}$ and ${bf k} + {bf K}$ are close to Fermi surface in the absence of SDW. At the mean field level, $A_k (omega)$ for such fermions has peaks at $omega = pm Delta (T)$ at $T < T_N$ and displays a conventional Fermi liquid behavior at $T > T_N$. We show that this behavior changes qualitatively beyond mean-field due to singular self-energy contributions from thermal fluctuations in a quasi-2D system. We use a non-perturbative eikonal approach and sum up infinite series of thermal self-energy terms. We show that $A_k (omega)$ shows peak/dip/hump features at $T < T_N$, with the peak position at $Delta (T)$ and hump position at $Delta (T=0)$. Above $T_N$, the hump survives up to $T = T_p > T_N$, and in between $T_N$ and $T_p$ the spectral function displays the pseudogap behavior. We show that the difference between $T_p$ and $T_N$ is controlled by the ratio of in-plane and out-of-plane static spin susceptibilities, which determines the combinatoric factors in the diagrammatic series for the self-energy. For certain values of this ratio, $T_p = T_N$, i.e., the pseudogap region collapses. In this last case, thermal fluctuations are logarithmically singular, yet they do not give rise to pseudogap behavior. Our computational method can be used to study pseudogap physics due to thermal fluctuations in other systems.
We study the effects of quantum fluctuations on a non-coplanar tetrahedral spin structure, which has a scalar chiral order, in the spin-1/2 multiple-spin exchange model with up to the six-spin exchange interactions on a triangular lattice. We find that, in the linear spin-wave approximation, the tetrahedral structure survives the quantum fluctuations because spin waves do not soften in the whole parameter region of the tetrahedral-structure phase evaluated for the classical system. In the quantum corrections to the ground-state energy, sublattice magnetization, and scalar chirality, the effects of the quantum fluctuations are small for the ferromagnetic nearest-neighbor interactions and for the strong five-spin interactions. The six-spin interactions have little effect on the quantum corrections in the tetrahedral-structure phase. This calculation also corrects an error in the previously reported value of scalar chirality for the spin-1/2 multiple-spin exchange model with up to the four-spin exchange interactions.
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