Ground State Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Spin Wave Approximation-

Matsuda, T.; Hida, Kazuo

doi:10.1143/jpsj.59.2223

Cited by 36 publications

(30 citation statements)

References 17 publications

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“…Our calculation complements previous calculations for Sϭ1/2 only and/or using additional approximations, as well as a calculation using the related Takahasi bosons approach. [4][5][6] Our results show that the transition from the AF ordered state to disordered state is second order for small S, and first order for large S. A simple argument using spinwave theory helps to explain why a first-order transition occurs for large S. In the latter case, the magnetization decreases slowly as the interplane coupling J Ќ increases, and it remains finite when the IVBS becomes lower in energy. Quantitatively the critical S separating first from secondorder transition S c , is found to be 0.35 within the mean-field theory ͑MFT͒.…”

Section: Introductionmentioning

confidence: 66%

“…We can understand why large S favors a first-order transition quite simply in terms of spin-wave theory. 4,5 The Néel state energy is E N ϭS 2 (2JzϩJ Ќ ) while the energy of the IVBS state is E V ϭJ Ќ S(Sϩ1). Equating the two implies an estimate for the first-order transition at ␤ 1 of the order of S for large S. Within spin-wave theory, the sublattice magnetization is given by m s in Eq.…”

Section: Discussionmentioning

confidence: 99%

“…Since the spin is quantized, the spin value cannot be decreased beyond 1/2, hence the model does not have a spin-liquid ground state. On the other hand, when two planes of antiferromagnetic spins are coupled together, [3][4][5][6][7][8][9][10][11] and if the interplane coupling is strong enough, the ground state is easily seen to be one of valence bond solid of interplane singlets ͑IVBS͒. Thus, there should be a transition from the LRO Néel state to a spinliquid state as the interplane coupling is increased.…”

Section: Introductionmentioning

confidence: 99%

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Phase transitions of the bilayered spin-SHeisenberg model

Zhang

1996

Phys. Rev. B

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We study the ground state and the phase transitions of the bilayered spin-S antiferromagnetic Heisenberg model using the Schwinger boson mean-field theory. The interplane coupling initially stabilizes but eventually destroys the long-range antiferromagnetic order. The transition to the disordered state is continuous for small S, and first order for large S. The latter is consistent with an argument based on spin-wave theory. ͓S0163-1829͑96͒01818-8͔

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Section: Introductionmentioning

confidence: 66%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase transitions of the bilayered spin-SHeisenberg model

Zhang

1996

Phys. Rev. B

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“…1,2,3,4) It is, however, expected that the strong quantum fluctuation in this system may lead to the destruction of the long range order with the help of some additional mechanism. In this context, the square lattice antiferromagnetic Heisenberg model with nearest and nextnearest exchange interaction (hereafter called J 1 -J 2 model) 5,6,3,4,7,8,9,10,11,12,13,14,15,16,17,18) and the bilayer Heisenberg model 19,20,21,22,23,24,25,26,27,28) have been studied extensively. Considering the difference of the nature of the mechanism leading to the spin-gap phase in these two models, it must be most interesting to study their interplay in the bilayer J 1 -J 2 model.…”

Section: §1 Introductionmentioning

confidence: 99%

Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Hida

1998

J. Phys. Soc. Jpn.

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The ground state of the square lattice bilayer quantum antiferromagnet with nearest (J1) and next-nearest (J2) neighbour intralayer interaction is studied by means of the dimer expansion method up to the 6-th order in the interlayer exchange coupling J3. The phase boundary between the spin-gap phase and the magnetically ordered phase is determined from the poles of the biased Padé approximants for the susceptibility and the inverse energy gap assuming the universality class of the 3-dimensional classical Heisenberg model. For weak frustration, the critical interlayer coupling decreases linearly with α(= J2/J1). The spin-gap phase persists down to J3 = 0 (single layer limit) for 0.45 < ∼ α < ∼ 0.65. The crossover of the short range order within the disordered phase is also discussed.KEYWORDS: bilayer Heisenberg antiferromagnet, frustration, Padé approximant, dimer expansion method, spingap state §1. IntroductionThe spin-1/2 square lattice Heisenberg model is now widely believed to have an antiferromagnetic long range order in the ground state.1, 2, 3, 4) It is, however, expected that the strong quantum fluctuation in this system may lead to the destruction of the long range order with the help of some additional mechanism. In this context, the square lattice antiferromagnetic Heisenberg model with nearest and nextnearest exchange interaction (hereafter called J 1 -J 2 model) 5,6,3,4,7,8,9,10,11,12,13,14,15,16,17,18) and the bilayer Heisenberg model 19,20,21,22,23,24,25,26,27,28) have been studied extensively. Considering the difference of the nature of the mechanism leading to the spin-gap phase in these two models, it must be most interesting to study their interplay in the bilayer J 1 -J 2 model. 30, 29)In the bilayer model, if the interlayer antiferromagnetic coupling is strong enough, the spins on both layers form interlayer singlet pairs and the quantum fluctuation is enhanced leading to the quantum disordered state. The dimer expansion study of this model has been quite successful 21,24,25,26,27) and it is shown that the transition between the Néel phase and the spin-gap phase belongs to the universality class of 3-dimensional classical Heisenberg model. This result is also confirmed by quantum Monte Carlo simulation. 23)On the other hand, in the J 1 -J 2 model, the competition between the nearest neighbour interaction J 1 and the nearest neighbour interaction J 2 introduces the frustration in the spin configuration which enhances the quantum fluctuation. The conclusion about the presence of the quantum disordered state in this model is, however, still controversial even in the most frustrated * e-mail: hida@riron.ged.saitama-u.ac.jp regime.In order to apply the dimer expansion method to the single layer J 1 -J 2 model, it is inevitable to start with the dimer configurations which break the translational symmetry as an unperturbed ground state.3, 4) In the bilayer J 1 -J 2 model, the unperturbed ground state can be taken as the interlayer dimers and the translational symmetry of the original Hamiltonian is ...

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“…We show that the critical coupling decreases linearly with frustration. The model of two coupled antiferromagnetic layers, the 'bilayer model', has attracted much attention in the last years [1][2][3]. The physics of this model is dominated by the competition between the in-plane coupling J || and the inter-plane coupling J 12 .…”

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confidence: 99%

The Transition from an Ordered Antiferromagnet to a Quantum Disordered Spin Liquid in a Solvable Bilayer Model

Gros¹,

Wenzel²,

Richter³

1995

Europhys. Lett.

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We present a spin-1/2 bilayer model for the quantum order-disorder transition which (i) can be solved by mean-field theory for bulk quantities, (ii) becomes critical at the transition, and (iii) allows to include intralayer frustration. We present numerical data (for systems with up to 240 sites) and analytical results for the critical coupling strength, groundstate energy, order parameter and for the gap. We show that the critical coupling decreases linearly with frustration. The model of two coupled antiferromagnetic layers, the 'bilayer model', has attracted much attention in the last years [1][2][3]. The physics of this model is dominated by the competition between the in-plane coupling J || and the inter-plane coupling J 12 . A transition occurs from an ordered antiferromagnetic state to a spin-liquid state with a gap at a certain critical ratio J c of J 12 /J || . Millis and Monien [4] proposed that certain anomalies in the magnetic response of Y Ba 2 Cu 3 O 6+x , interpreted commonly as evidence for a spin gap might be explained within the bilayer model. Solvable model Hamiltonians play an important role in condensed matter theory, as they provide new insights and because they can be used as references for approximate theories. Here we propose a non-trivial 'long-range' version of the bilayer model for which we are able to solve for all quantities of interest, while retaining the crucial ingredients driving the quantum order-disorder transition. In this model the in-plane coupling J 1 is of longrange Lieb-Mattis type while the inter-plane coupling, J 12 , remains short ranged. As a result, bulk expectation values for this system are accessible by analytical considerations, we are able to determine the exact groundstate wavfunction up to intensive corrections. Excitations, remain non-trivial however, but the simplicity of the in-plane interaction facilitates the numerical analysis to obtain excellent control over finite size corrections. We determine the functional dependence of the gap as a function of J 12 /J 1 , presenting the first rigorous study of the impact of in-plane frustration on the stability of the spin-liquid phase. We find that the critical J c is reduced linearly with the in-plane frustration [5,6]. This result is of particular interest since a substantial interlayer coupling constant J 12 was found in recent infrared absorption experiments on Y 1 Ba 2 Cu 3 O 6 [7] and by a detailed quantum chemical calculation [8,9].Model: We define the 'long-range' bilayer Hamiltonian as H LR = γ H γ + H 12 , withand J 1 , J 2 , J 12 > 0. Here S i,γ are the spin-1/2 operators of the first (γ = 1) and of the second (γ = 2) layer respectively and S Aγ = i∈A S i,γ , S Bγ = i∈B S i,γ are the total-spin operators of the A/B sublattice in the respective layers. Each sublattice contains N spins, the total number of sites is N s = 4N .The first term of the intra-layer interaction (J 1 ), favours an anti-alignment of the sublattice spins, i.e. an antiferromagnetically ordered state. The second, frustrating, intra-...

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Ground State Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Spin Wave Approximation-

Cited by 36 publications

References 17 publications

Phase transitions of the bilayered spin-SHeisenberg model

Phase transitions of the bilayered spin-SHeisenberg model

Dimer Expansion Study of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

The Transition from an Ordered Antiferromagnet to a Quantum Disordered Spin Liquid in a Solvable Bilayer Model

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