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Bishop, R. F.; Farnell, Damian J. J.; Parkinson, John

doi:10.1103/physrevb.58.6394

Cited by 102 publications

(142 citation statements)

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“…2-4, is not appropriate for the 3d problem under consideration. Therefore, we use the coupled-cluster method (CCM) 6,[20][21][22][23][24] and the rotationinvariant Green's function method (RGM). 5,17,26,[28][29][30] Both methods have been successfully applied to quantum spin systems in arbitrary dimension and are able to deal with frustration.…”

Section: 14mentioning

confidence: 99%

“…Though we start our CCM calculation with a reference state corresponding to semiclassical order, one can compute the GS energy also in parameter regions where semiclassical magnetic LRO is destroyed, and it is known 6,[22][23][24] that the CCM yields precise results for the GS energy beyond the transition from the semiclassical magnetic phase to the quantum paramagnetic phase. The necessary condition for the convergence of the CCM equations is a sufficient overlap between the reference state and the true GS.…”

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confidence: 99%

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QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

et al. 2006

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Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling J ⊥ on the magnetic ordering in the ground state of the spin-1/2 J1-J2 frustrated Heisenberg antiferromagnet (J1-J2 model) on the stacked square lattice. In agreement with known results for the J1-J2 model on the strictly two-dimensional square lattice (J ⊥ = 0) we find that the phases with magnetic long-range order at small J2 < Jc 1 and large J2 > Jc 2 are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling J ⊥ > 0 the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small J ⊥ ∼ 0.2 − 0.3J1.The properties of the frustrated spin-1/2 Heisenberg antiferromagnet (HAFM) with nearest-neighbor J 1 and competing next-nearest-neighbor J 2 coupling (J 1 -J 2 model) on the square lattice have attracted a great deal of interest during the last fifteen years (see, e.g., Refs. 1-12 and references therein). The recent synthesis of layered magnetic materials 13,14 which can be described by the J 1 -J 2 model has stimulated a renewed interest in this model. It is well-accepted that the model exhibits two magnetically long-range ordered phases at small and at large J 2 separated by an intermediate quantum paramagnetic phase without magnetic long-range order (LRO) in the parameter region J c1 < J 2 < J c2 , where J c1 ≈ 0.4 and J c2 ≈ 0.6. The ground state (GS) at low J 2 < J c1 exhibits semi-classical Néel magnetic LRO with the magnetic wave vector Q 0 = (π, π). The GS at large J 2 > J c2 shows so-called collinear magnetic LRO with the magnetic wave vectors Q 1 = (π, 0) or Q 2 = (0, π). These two collinear states are characterized by a parallel spin orientation of nearest neighbors in vertical (horizontal) direction and an antiparallel spin orientation of nearest neighbors in horizontal (vertical) direction. The properties of the intermediate quantum paramagnetic phase are still under discussion, however, a valence-bond crystal phase seems to be most favorable. 2-4,8,9The properties of quantum magnets strongly depend on the dimensionality.15 Though the tendency to order is more pronounced in three-dimensional (3d) systems than in low-dimensional ones, a magnetically disordered phase can also be observed in frustrated 3d systems such as the HAFM on the pyrochlore lattice 16 or on the stacked kagomé lattice.17 On the other hand, recently it has been found that the 3d J 1 -J 2 model on the body-centered cubic lattice does not have an intermediate quantum paramagnetic phase.18,19 Moreover, in experimental realizations of the J 1 -J 2 model the magnetic couplings are expected to be not strictly 2d, but a finite interlayer coupling J ⊥ is present. For example, recently Rosner et al.14 have found J ⊥ /J 1 ∼ 0.07 for Li 2 VOSiO 4 , a material which can be described by a square lattice J 1 -J 2 model with large J 2 . 13,14This motivates us to consider an extension of the...

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Section: 14mentioning

confidence: 99%

mentioning

confidence: 99%

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

et al. 2006

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“…In fact, in the case S = 1 2 various numerical studies including exact diagonalization, [18][19][20][21] variational Monte Carlo 22,23 series expansion [24][25][26][27][28] as well as the coupled cluster approach 29 give the consistent picture that in the regime 0.4Շ J 2 / J 1 Շ 0.6 no magnetic order is present clearly indicating that the aforementioned semiclassical treatments overestimate the stability of the ordered states. Another key observation of the series expansion and in particular of the unbiased exact diagonalization studies is that in the paramagnetic phase the lattice symmetry is spontaneously broken due to the formation of columnar valence-bond solid order.…”

Section: Introductionmentioning

confidence: 99%

Phase diagram of the frustrated spatially-anisotropicS=1antiferromagnet on a square lattice

et al. 2009

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We study the S = 1 square lattice Heisenberg antiferromagnet with spatially anisotropic nearest-neighbor couplings J 1x and J 1y frustrated by a next-nearest-neighbor coupling J 2 numerically using the density-matrix renormalization-group ͑DMRG͒ method and analytically employing the Schwinger-Boson mean-field theory ͑SBMFT͒. Up to relatively strong values of the anisotropy, within both methods we find quantum fluctuations to stabilize the Néel-ordered state above the classically stable region. Whereas SBMFT suggests a fluctuationinduced first-order transition between the Néel state and a stripe antiferromagnet for 1 / 3 Յ J 1x / J 1y Յ 1 and an intermediate paramagnetic region opening only for very strong anisotropy, the DMRG results clearly demonstrate that the two magnetically ordered phases are separated by a quantum-disordered region for all values of the anisotropy with the remarkable implication that the quantum paramagnetic phase of the spatially isotropic J 1 -J 2 model is continuously connected to the limit of decoupled Haldane spin chains. Our findings indicate that for S = 1 quantum fluctuations in strongly frustrated antiferromagnets are crucial and not correctly treated on the semiclassical level.

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“…28 Subsequently, high-order CCM approximations have been applied to the XXZ model, 28 the anisotropic XY model 26 and the J 1 -J 2 model. 7 In addition to the CCM results we also present variational, spin-wave theory (SWT) and exact diagonalization (ED) results for the sake of comparison.…”

Section: Introductionmentioning

confidence: 99%

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

Krüger¹,

Richter²,

Schulenburg³

et al. 2000

Phys. Rev. B

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105

272

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We study the zero-temperature phase diagram and the low-lying excitations of a square-lattice spinhalf Heisenberg antiferromagnet with two types of regularly distributed nearest-neighbour exchange bonds (J > 0 (antiferromagnetic) and −∞ < J ′ < ∞) using the coupled cluster method (CCM) for high orders of approximation (up to LSUB8). We use a Néel model state as well as a helical model state as a starting point for the CCM calculations. We find a second-order transition from a phase with Néel order to a finite-gap quantum disordered phase for sufficiently large antiferromagnetic exchange constants J ′ > 0. For frustrating ferromagnetic couplings J ′ < 0 we find indications that quantum fluctuations favour a first-order phase transition from the Néel order to a quantum helical state, by contrast with the corresponding second-order transition in the corresponding classical model. The results are compared to those of exact diagonalizations of finite systems (up to 32 sites) and those of spin-wave and variational calculations. The CCM results agree well with the exact diagonalization data over the whole range of the parameters. The special case of J ′ = 0, which is equivalent to the honeycomb lattice, is treated more closely.

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Phase transitions in the spin-halfJ1−J2model

Cited by 102 publications

References 47 publications

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

QuantumJ1−J2Antiferromagnet on a Stacked Square Lattice: Influence of the Interlayer Coupling on the Ground-State Magnetic Ordering

Phase diagram of the frustrated spatially-anisotropicS=1antiferromagnet on a square lattice

Quantum phase transitions of a square-lattice Heisenberg antiferromagnet with two kinds of nearest-neighbor bonds: A high-order coupled-cluster treatment

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