R. Darradi

Coupled cluster treatment of the Shastry-Sutherland antiferromagnet

We consider the zero-temperature properties of the spin-half two-dimensional Shastry-Sutherland antiferromagnet by using a high-order coupled cluster method treatment. We find that this model demonstrates various ground-state phases (Neel, magnetically disordered, orthogonal dimer), and we make predictions for the positions of the phase transition points. In particular, we find that the orthogonal-dimer state becomes the ground state at J2d∕J1∼1.477. For the critical point J2c∕J1 where the semiclassical Neel order disappears we obtain a significantly lower value than J2d∕J1, namely, J2c∕J1 in the range 1.14–1.39. We therefore conclude that an intermediate phase exists between the Neel and the dimer phases. An analysis of the energy of a competing spiral phase yields clear evidence that the spiral phase does not become the ground state for any value of J2. The intermediate phase is therefore magnetically disordered but may exhibit plaquette or columnar dimer ordering.

The effect of anisotropy on the ground-state magnetic ordering of the spin-1 quantum J1XXZ–J2XXZ model on the square lattice

We study the zero-temperature phase diagram of the J XXZ 1 -J XXZ 2 Heisenberg model for spin-1 particles on an infinite square lattice interacting via nearest-neighbour (J1 ≡ 1) and next-nearest-neighbour (J2 > 0) bonds. The two bonds have the same XXZ -type anisotropy in spin space. The effects on the quasiclassical Neel-ordered and collinear stripe-ordered states of varying the anisotropy parameterare investigated using the coupled cluster method carried out up to high orders. By contrast with the case for spin- 1 particles studied previously, no intermediate disordered phase between the Neel and collinear stripe phases, for any value of the frustration J2/J1, for either the z-aligned ( �> 1) or xy -planar-aligned (0 �< 1) states, is predicted here. The quantum phase transition is determined as first order for all values of J2/J1

Quantum phases of the planar antiferromagneticJ1−J2−J3Heisenberg model

We present results of a complementary analysis of the frustrated planar J_1-J_2-J_3 spin-1/2 quantum-antiferromagnet. Using dynamical functional renormalization group, high-order coupled cluster calculations, and series expansion based on the flow equation method, we have calculated generalized momentum resolved susceptibilities, the ground state energy, the magnetic order parameter, and the elementary excitation gap. From these we determine a quantum phase diagram which shows a large window of a quantum paramagnetic phase situated between the Neel, spiral and collinear states, which are present already in the classical J_1-J_2-J_3 antiferromagnet. Our findings are consistent with substantial plaquette correlations in the quantum paramagnetic phase. The extent of the quantum paramagnetic region is found to be in satisfying agreement between the three different approaches we have employed.

Frustrated quantum antiferromagnets: Application of high-order coupled cluster method

We report on recent results for strongly frustrated quantum J1 - J2 antiferromagnets in dimensionality d = 1, 2, 3 obtained by the coupled cluster method (CCM). We demonstrate that the CCM in high orders of approximation allows us to investigate quantum phase transitions driven by frustration and to discuss novel quantum ground states. In detail we consider the ground-state properties of (i) the Heisenberg spin-1/2 antiferromagnet on the cubic lattice in d = 1, 2, 3, and use the results for the energy, the sublattice magnetization and the spin stiffness as a benchmark test for the precision of the method; (ii) coupled frustrated spin chains (the quasi-one-dimensional J1 - J2 model) and discuss the influence of the quantum fluctuations and the interchain coupling on the incommensurate spiral state present in the classical model; (iii) the Shastry-Sutherland antiferromagnet on the square lattice; and (iv) a stacked frustrated square-lattice Heisenberg antiferromagnet (the quasi-two-dimensional J1 - J2 model), and discuss the influence of the interlayer coupling on the quantum paramagnetic ground-state phase that is present for the strictly two-dimensional model.

Spin-half Heisenberg antiferromagnet on two archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond

We investigate the ground state of the two-dimensional Heisenberg antiferromagnet on two Archimedean lattices, namely, the maple-leaf and bounce lattices as well as a generalized J-J′ model interpolating between both systems by varying J′/J from J′/J=0 (bounce limit) to J′/J=1 (maple-leaf limit) and beyond. We use the coupled cluster method to high orders of approximation and also exact diagonalization of finite-sized lattices to discuss the ground-state magnetic long-range order based on data for the ground-state energy, the magnetic order parameter, the spin-spin correlation functions as well as the pitch angle between neighboring spins. Our results indicate that the “pure” bounce (J′/J=0) and maple-leaf (J′/J=1) Heisenberg antiferromagnets are magnetically ordered, however, with a sublattice magnetization drastically reduced by frustration and quantum fluctuations. We found that magnetic long-range order is present in a wide parameter range 0⩽J′/J≲J′c/J and that the magnetic order parameter varies only weakly with J′/J. At J′c≈1.45J, a transition to a quantum orthogonal-dimer singlet ground state without magnetic long-range order takes place that is probably of first-order type, although we cannot rule out that this transition is second order. The orthogonal-dimer state is the exact ground state in this large-J′ regime, and so our model has similarities to the Shastry-Sutherland model. Finally, we use the exact diagonalization to investigate the magnetization curve. We find a 1/3 magnetization plateau for J′/J≳1.07 and another one at 2/3 of saturation emerging only at large J′/J≳3.

Direct calculation of the spin stiffness of the spin-12 Heisenberg antiferromagnet on square, triangular, and cubic lattices using the coupled-cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.

The spin-half XXZ antiferromagnet on the square lattice revisited: A high-order coupled cluster treatment

We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half {\it XXZ} antiferromagnet on the square lattice. The CCM is applied to it to high orders of approximation by using an efficient computer code that has been written by us and which has been implemented to run on massively parallelized computer platforms. We are able therefore to present precise data for the basic quantities of this model over a wide range of values for the anisotropy parameter Δ in the range −1≤Δ 1) regimes, where Δ→∞ represents the Ising limit. We present results for the ground-state energy, the sublattice magnetization, the zero-field transverse magnetic susceptibility, the spin stiffness, and the triplet spin gap. Our results provide a useful yardstick against which other approximate methods and/or experimental studies of relevant antiferromagnetic square-lattice compounds may now compare their own results. We also focus particular attention on the behaviour of these parameters for the easy-axis system in the vicinity of the isotropic Heisenberg point (Δ=1), where the model undergoes a phase transition from a gapped state (for Δ>1) to a gapless state (for Δ≤1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at Δ=1 for the present model with spins of spin quantum number s=12 that is revealed by our CCM results seems to differ qualitatively from that predicted by SWT, which becomes exact only for its near-classical large-s counterpart.

Direct calculation of the spin stiffness on square, triangular and cubic lattices using the coupled cluster method

We present a method for the direct calculation of the spin stiffness by means of the coupled cluster method. For the spin-half Heisenberg antiferromagnet on the square, the triangular and the cubic lattices we calculate the stiffness in high orders of approximation. For the square and the cubic lattices our results are in very good agreement with the best results available in the literature. For the triangular lattice our result is more precise than any other result obtained so far by other approximate method.