Coupled-cluster treatments of correlations in quantum antiferromagnets

Bishop, R. F.; Parkinson, John; Xian, Yang

doi:10.1103/physrevb.44.9425

Cited by 96 publications

(135 citation statements)

References 63 publications

(1 reference statement)

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“…The order parameter M is given by the expectation value of s z i . For the considered quantum many-body model it is necessary to use approximations in order to truncate the expansion of S. We use the well elaborated LSUBn scheme 20,21,23 in which in the correlation operator S all multi-spin correlations over all distinct locales on the lattice defined by n or fewer contiguous sites are taken into account. For example, within the LSUB4 scheme one includes multi-spin creation operators of one, two, three or four spins distributed on arbitrary clusters of four contiguous lattice sites.…”

Section: 14mentioning

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%

“…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%

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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“…Following Emrich in the traditional CCM [13,14], we express excitation ket-state |Ψ e by a linear operator X constructed from creation operators acting onto the ground state |Ψ g as…”

Section: Quasiparticle Excitationsmentioning

confidence: 99%

“…We investigate two different types of excitation states using two approaches. In the first approach, we follow the traditional CCM [13,14] to investigate quasiparticle excitations, but keeping our ket and bra excited states hermitian to one another. We then investigate collective modes by adapting Feynman's excitation theory of phonon-roton spectrum of helium liquid [15] to our method.…”

Section: Introductionmentioning

confidence: 99%

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

Xian¹

2007

J. Phys.: Condens. Matter

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We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin ±1. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.

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“…For the quasiparticle excitations, briefly, we follow Emrich in the traditional CCM [20,21] and write excitation ket-state |Ψ e involving only C † I operators as…”

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confidence: 99%

Variational coupled-cluster study of plasmonlike excitations in quantum antiferromagnets

Xian

2006

Phys. Rev. B

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We extend recently proposed variational coupled-cluster method to describe excitation states of quantum antiferromagnetic bipartite lattices. We reproduce the spin-wave excitations (i.e., magnons with spin ±1). In addition, we obtain a new, spin-zero excitation (magnon-density waves) which has been missing in all existing spin-wave theories. Within our approximation, this magnon-densitywave excitation has a nonzero energy gap in a cubic lattice and is gapless in a square lattice, similar to those of charge-density-wave excitations (plasmons) in quantum electron gases.PACS numbers: 31.15. Dv, 75.10.Jm, 75.30.Ds, 75.50.Ee From many-body physics view, energy spectra of lowlying excitation states of a quantum many-body interacting system are mainly determined by the correlations included in its ground state. Feynman's description of the phonon-roton excitations in a Helium-4 quantum liquid is a well-known example [1,2]. For the ground state properties, the method of correlated basis functions (CBF) has produced satisfactory results. Combining with Feynman's excitation theory, we therefore have an analytical, systematic method capable of describing most states of the Helium-4 quantum liquid at low temperature [2].The coupled-cluster method (CCM) [3,4,5] is another successful microscopic many-body theory which has produced many most competitive results for the ground state properties of many atoms, molecules, electron gas, and quantum spin systems [6]. In the traditional CCM, however, the bra and ket states are not hermitian to one another [7]. We recently extended the CCM to a variational formalism [8,9], in which bra and ket states are hermitian to one another. In our analysis, a close relation with the CBF method was found and exploited by using diagrammatic techniques. In application to quantum antiferromagnets, our calculations in a simple approximation reproduced the ground state properties of the spin-wave theory (SWT) [10]. Improvements over SWT by higherorder calculations were also obtained [9]. Here we extend this variational method to describe excitation states. Inspired by the close relation to the CBF method, we are able to obtain the energy spectra of quasiparticle-densitywave excitations by following Feynman, as well as the usual quasiparticle excitation spectra as in the traditional CCM. For the antiferromagnetic models, these quasiparticle excitations correspond to the well known spin-wave excitations (magnons) with spin ±1; the new, spin-zero excitations are identified as magnon-density-wave excitations whose energy spectra share some characteristics with that of charge-density-wave excitations (plasmons) in quantum electron gases [11]. We like to emphasize that these spin-zero excitations have been missing in all spinwave theories, including the more recently modified spinwave theories [12,13,14]. Magnon-density fluctuations in Heisenberg ferromagnets at low temperature were investigated in the sixties by calculating the longitudinal susceptibility [15,16]. Calculations for the longitudinal spin ...

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Coupled-cluster treatments of correlations in quantum antiferromagnets

Cited by 96 publications

References 63 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

Excited states of quantum many-body interacting systems: a variational coupled-cluster description

Variational coupled-cluster study of plasmonlike excitations in quantum antiferromagnets

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