Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number s

Götze, O.; Richter, Johannes; Zinke, Ronald; Farnell, Damian J. J.

doi:10.1016/j.jmmm.2015.08.113

Cited by 33 publications

(45 citation statements)

References 91 publications

(203 reference statements)

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“…The spin stiffness ρ s measures the increase in the amount of energy as we twist the magnetic order parameter of a magnetically long-range ordered system along a given direction by a small angle θ per unit length, see, e.g., Refs. [72,[77][78][79][80]. We use here the notations given in Ref.…”

Section: Discussionmentioning

confidence: 99%

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Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

2016

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The J 1 -J 2 Heisenberg model is a "canonical" model in the field of quantum magnetism in order to study the interplay between frustration and quantum fluctuations as well as quantum phase transitions driven by frustration. Here we apply the Coupled Cluster Method (CCM) to study the spin-half J 1 -J 2 model with antiferromagnetic nearest-neighbor bonds J 1 > 0 and next-nearestneighbor bonds J 2 > 0 for the simple cubic (SC) and body-centered cubic (BCC) lattices. In particular, we wish to study the ground-state ordering of these systems as a function of the frustration parameter p = z 2 J 2 /z 1 J 1 , where z 1 (z 2 ) is the number of nearest (next-nearest) neighbors.We wish to determine the positions of the phase transitions using the CCM and we aim to resolve the nature of the phase transition points. We consider the ground-state energy, order parameters, spin-spin correlation functions as well as the spin stiffness in order to determine the ground-state phase diagrams of these models. We find a direct first-order phase transition at a value of p = 0.528 from a state of nearest-neighbor Néel order to next-nearest-neighbor Néel order for the BCC lattice.For the SC lattice the situation is more subtle. CCM results for the energy, the order parameter, the spin-spin correlation functions and the spin stiffness indicate that there is no direct first-order transition between ground-state phases with magnetic long-range order, rather it is more likely that

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Section: Discussionmentioning

confidence: 99%

“…1b). For the classical model in the AF1 phase we easily obtain [17,72,75,80]. We introduce the twist as described above and use the twisted state as the model state for the CCM calculation.…”

Section: Discussionmentioning

confidence: 99%

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

2016

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“…[43,53] for the square-and triangular-lattice Heisenberg antiferromagnet. However, it is useful to note here briefly that we add an appropriate transverse magnetic field term to the Hamiltonian of Eq.…”

Section: The Ccm Applied To the Xxz Modelmentioning

confidence: 99%

“…The precise nature of the canted model states and the solution of the associated CCM problem is described in detail in Refs. [43,53]. The uniform transverse magnetic susceptibility is then defined as usual by the relation…”

Section: The Ccm Applied To the Xxz Modelmentioning

confidence: 99%

“…2, as a final step we need to extrapolate our LSUBm estimates for all physical quantities to the limit m → ∞ where the method becomes exact. Although exactly provable rules are not known for these extrapolations, robust empirical rules do exist, and these rules have successfully been tested for a wide range of quantum magnetic systems [33,35,38,39,43,51,53]. We use the "standard" rules in order to extrapolate all expectation values, namely: the ground-state energy per spin…”

Section: The Ccm Applied To the Xxz Modelmentioning

confidence: 99%

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

Bishop

Zinke

et al. 2017

Journal of Magnetism and Magnetic Materials

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We use the coupled cluster method (CCM) to study the ground-state properties and lowest-lying triplet excited state of the spin-half 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 ∆ in the range −1 ≤ ∆ < ∞ of interest, including both the easy-plane (−1 < ∆ < 1) and easy-axis (∆ > 1) regimes, where ∆ → ∞ 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 (∆ = 1), where the model undergoes a phase transition from a gapped state (for ∆ > 1) to a gapless state (for ∆ ≤ 1), and compare our results there with those from spin-wave theory (SWT). Interestingly, the nature of the criticality at ∆ = 1 for the present model with spins of spin quantum number s = 1 2 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.

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Large-s expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number s

Bishop

2016

Journal of Magnetism and Magnetic Materials

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The coupled cluster method (CCM) is employed to very high orders of approximation to study the ground-state (GS) properties of the spin-s Heisenberg antiferromagnet (with isotropic interactions, all of equal strength, between nearest-neighbour pairs only) on the honeycomb lattice. We calculate with high accuracy the complete set of GS parameters that fully describes the low-energy behaviour of the system, in terms of an effective magnon field theory, viz., the energy per spin, the magnetic order parameter (i.e., the sublattie magnetization), the spin stiffness and the zero-field (uniform, transverse) magnetic susceptibility, for all values of the spin quantum number s in the range 1 2 ≤ s ≤ 9 2 . The CCM data points are used to calculate the leading quantum corrections to the classical (s → ∞) values of these low-energy parameters, considered as large-s asymptotic expansions.

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Ground-state properties of the triangular-lattice Heisenberg antiferromagnet with arbitrary spin quantum number s

Cited by 33 publications

References 91 publications

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

Ground-state ordering of theJ1−J2model on the simple cubic and body-centered cubic lattices

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

Large-s expansions for the low-energy parameters of the honeycomb-lattice Heisenberg antiferromagnet with spin quantum number s

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