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      High-Order Coupled Cluster Method Study of Frustrated and Unfrustrated Quantum Magnets in External Magnetic Fields

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          Abstract

          We apply the coupled cluster method (CCM) in order to study the ground-state properties of the (unfrustrated) square-lattice and (frustrated) triangular-lattice spin-half Heisenberg antiferromagnets in the presence of external magnetic fields. Here we determine and solve the basic CCM equations by using the localised approximation scheme commonly referred to as the `LSUB\(m\)' approximation scheme and we carry out high-order calculations by using intensive computational methods. We calculate the ground-state energy, the uniform susceptibility, the total (lattice) magnetisation and the local (sublattice) magnetisations as a function of the magnetic field strength. Our results for the lattice magnetisation of the square-lattice case compare well to those results of QMC for all values of the applied external magnetic field. We find a value for magnetic susceptibility of \(\chi=0.070\) for the square-lattice antiferromagnet, which is also in agreement with the results of other approximate methods (e.g., \(\chi=0.0669\) via QMC). Our estimate for the range of the extent of the (\(M/M_s=\))\(\frac 13\) magnetisation plateau for the triangular-lattice antiferromagnet is \(1.37< \lambda < 2.15\), which is in good agreement with results of spin-wave theory (\(1.248 < \lambda < 2.145\)) and exact diagonalisations (\(1.38 < \lambda < 2.16\)). The CCM value for the in-plane magnetic susceptibility per site is \(\chi=0.065\), which is below the result of the spin-wave theory (evaluated to order 1/S) of \(\chi_{SWT}=0.0794\).

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          Magnetization plateaus in frustrated antiferromagnetic quantum spin models

          Plateaus can be observed in the zero-temperature magnetization curve of quantum spin systems at rational values of the magnetization. In one dimension, the appearance of a plateau is controlled by a quantization condition for the magnetization which involves the length of the local spin and the volume of a translational unit cell of the ground state. We discuss examples of geometrically frustrated quantum spin systems with large (in general unbounded) periodicities of spontaneous breaking of translational symmetry in the ground state. In two dimensions, we discuss the square, triangular and Kagome lattices using exact diagonalization (ED) for up to N=40 sites. For the spin-1/2 XXZ model on the triangular lattice we study the nature and stability region of a plateau at one third of the saturation magnetization. The Kagome lattice gives rise to particularly rich behaviour with several plateaus in the magnetization curve and a jump due to local magnon excitations just below saturation.
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            Quantum stabilization of 1/3-magnetization plateau in Cs_2CuBr_4

            We consider the phase diagram of a spatially anisotropic 2D triangular antiferromagnet in a magnetic field. Classically, the ground state is umbrella-like for all fields, but we show that the quantum phase diagram is much richer and contains a 1/3 magnetization plateau, two commensurate planar states, two incommensurate chiral umbrella phases, and, possibly, a planar state separating the two chiral phases. Our analysis sheds light on several recent experimental findings for the spin-1/2 system Cs_2CuBr_4.
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              A Comparative Study of the Magnetization Process of Two-Dimensional Antiferromagnets

              Plateaux in the magnetization curves of the square, triangular and hexagonal lattice spin-1/2 XXZ antiferromagnet are investigated. One finds a zero magnetization plateau (corresponding to a spin-gap) on the square and hexagonal lattice with Ising-like anisotropies, and a plateau with one third of the saturation magnetization on the triangular lattice which survives a small amount of easy-plane anisotropy. Here we start with transfer matrix computations for the Ising limit and continue with series in the XXZ-anisotropy for plateau-boundaries using the groundstates of the Ising limit. The main focus is then a numerical computation of the magnetization curves with anisotropies in the vicinity of the isotropic situation. Finally, we discuss the universality class associated to the asymptotic behaviour of the magnetization curve close to saturation, as observed numerically in two and higher dimensions.
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                Author and article information

                Journal
                20 August 2009
                Article
                10.1088/0953-8984/21/40/406002
                0908.2881
                17cde00d-c0f2-4a2c-ae0d-116e8750841a

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

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                Custom metadata
                J. Phys.: Condens. Matter 21 (2009) 406002
                30 pages, 13 figures, 1 Table
                cond-mat.str-el

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