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Register a new userQuantum order by disorder in the Kitaev model on a triangular lattice
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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.
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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.
We observe a disappearance of the 1/3 magnetization plateau and a striking change of the magnetic configuration under a moderate doping of the model triangular antiferromagnet RbFe(MoO4)2. The reason is an effective lifting of degeneracy of mean-field ground states by a random potential of impurities, which compensates, in the low temperature limit, the fluctuation contribution to free energy. These results provide a direct experimental confirmation of the fluctuation origin of the ground state in a real frustrated system. The change of the ground state to a least collinear configuration reveals an effective positive biquadratic exchange provided by the structural disorder. On heating, doped samples regain the structure of a pure compound thus allowing for an investigation of the remarkable competition between thermal and structural disorder.
We present a Quantum Monte Carlo study of the Ising model in a transverse field on a square lattice with nearest-neighbor antiferromagnetic exchange interaction J and one diagonal second-neighbor interaction $J$, interpolating between square-lattice ($J=0$) and triangular-lattice ($J=J$) limits. At a transverse-field of $B_x=J$, the disorder-line first introduced by Stephenson, where the correlations go from Neel to incommensurate, meets the zero temperature axis at $Japprox 0.7 J$. Strong evidence is provided that the incommensurate phase at larger $J$, at finite temperatures, is a floating phase with power-law decaying correlations. We sketch a general phase-diagram for such a system and discuss how our work connects with the previous Quantum Monte Carlo work by Isakov and Moessner for the isotropic triangular lattice ($J=J$). For the isotropic triangular-lattice, we also obtain the entropy function and constant entropy contours using a mix of Quantum Monte Carlo, high-temperature series expansions and high-field expansion methods and show that phase transitions in the model in presence of a transverse field occur at very low entropy.
We show that the topological Kitaev spin liquid on the honeycomb lattice is extremely fragile against the second-neighbor Kitaev coupling $K_2$, which has recently been shown to be the dominant perturbation away from the nearest-neighbor model in iridate Na$_2$IrO$_3$, and may also play a role in $alpha$-RuCl$_3$ and Li$_2$IrO$_3$. This coupling naturally explains the zigzag ordering (without introducing unrealistically large longer-range Heisenberg exchange terms) and the special entanglement between real and spin space observed recently in Na$_2$IrO$_3$. Moreover, the minimal $K_1$-$K_2$ model that we present here holds the unique property that the classical and quantum phase diagrams and their respective order-by-disorder mechanisms are qualitatively different due to the fundamentally different symmetries of the classical and quantum counterparts.
We study the half-filled Hubbard model on the triangular lattice with spin-dependent Kitaev-like hopping. Using the variational cluster approach, we identify five phases: a metallic phase, a non-coplanar chiral magnetic order, a $120^circ$ magnetic order, a nonmagnetic insulator (NMI), and an interacting Chern insulator (CI) with a nonzero Chern number. The transition from CI to NMI is characterized by the change of the charge gap from an indirect band gap to a direct Mott gap. Based on the slave-rotor mean-field theory, the NMI phase is further suggested to be a gapless Mott insulator with a spinon Fermi surface or a fractionalized CI with nontrivial spinon topology, depending on the strength of Kitaev-like hopping. Our work highlights the rising field that interesting phases emerge from the interplay of band topology and Mott physics.
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