Coordinate Bethe ansatz Computation for Low Temperature Behavior of a Triangular Lattice of a Spin-1 Heisenberg Antiferromagnet (original) (raw)
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The coupled cluster method (CCM) is used to study the zero-temperature properties of a frustrated spin-half (s = 1 2) J1-J2 Heisenberg antiferromagnet (HAF) on a two-dimensional (2D) chevron-square lattice. On an underlying square lattice each site of the model has 4 nearestneighbor exchange bonds of strength J1 > 0 and 2 frustrating next-nearest-neighbor (diagonal) bonds of strength J2 ≡ κJ1 > 0, such that each fundamental square plaquette has only one diagonal bond. The diagonal J2 bonds are arranged in a chevron pattern such that along one of the two basic square axis directions (say, along rows) the J2 bonds are parallel, while along the perpendicular axis direction (say, along columns) alternate J2 bonds are perpendicular to each other, and hence form one-dimensional (1D) chevron chains in this direction. The model thus interpolates smoothly between 2D HAFs on the square (κ = 0) and triangular (κ = 1) lattices, and also extrapolates to disconnected 1D HAF chains (κ → ∞). The classical (s → ∞) version of the model has collinear Néel order for 0 < κ < κ cl and a form of noncollinear spiral order for κ cl < κ < ∞, where κ cl = 1 2. For the s = 1 2 model we use both these classical states, as well as other collinear states not realized as classical ground-state (GS) phases, as CCM reference states, on top of which the multispin-flip configurations resulting from quantum fluctuations are incorporated in a systematic truncation hierarchy, which we carry out to high orders and then extrapolate to the physical limit. At each order we calculate the GS energy, GS magnetic order parameter, and the susceptibilities of the states to various forms of valence-bond crystalline (VBC) order, including plaquette and two different dimer forms. We find strong evidence that the s = 1 2 model has two quantum critical points, at κc 1 ≈ 0.72(1) and κc 2 ≈ 1.5(1), such that the system has Néel order for 0 < κ < κc 1 , a form of spiral order for κc 1 < κ < κc 2 that includes the correct three-sublattice 120 • spin ordering for the triangular-lattice HAF at κ = 1, and parallel-dimer VBC order for κc 2 < κ < ∞.
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Physics Letters A, 2005
The spin Green's function of the antiferromagnetic Heisenberg model on a triangular lattice is calculated using Mori's projection operator technique. At T = 0 the spin excitation spectrum is shown to have gaps at the wave vectors of the classical Néel ordering. This points to the absence of the antiferromagnetic long-range order in the ground state. The calculated spin correlation on the neighboring sites of the same sublattice is in good agreement with the value derived from exact diagonalization. The temperature dependencies of the spin correlations and the gaps are calculated.
Physical Review B, 2000
The spin fluctuations parallel to the external magnetic field in the ground state of the onedimensional (1D) s = 1 2 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization 0 < Mz < N/2, the ground state, which contains 2Mz spinons, is reconfigured as the physical vacuum for a different species of quasi-particles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasi-particles. For N → ∞, these collective excitations form a continuum in (q, ω)-space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor Szz(q, ω) are calculated directly from the Bethe wave functions for finite N . The resulting lineshape predictions for N → ∞ complement the exact results previously derived via algebraic analysis for the exact 2-spinon part of Szz(q, ω) in the zerofield limit. They are directly relevant for the interpretation of neutron scattering data measured in nonzero field on quasi-1D antiferromagnetic compounds.
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Journal of Magnetism and Magnetic Materials, 2013
Motivated by the fact that the study of disordered phases at zero temperature is of great interest, I study the spin-one quantum antiferromagnet with a next-nearest neighbor interaction on a triangular lattice with bilinear and biquadratic exchange interactions and a single ion anisotropy, using a SU(3) Schwinger boson mean-field theory. I calculate the critical properties, at zero temperature, for values of the single ion anisotropy parameter D above a critical value D C , where a quantum phase transition takes place from a higher D disordered phase to a lower D ordered phase.