Low Temperature Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Modified Spin Wave Method-

Hida, Kazuo

doi:10.1143/jpsj.59.2230

Cited by 56 publications

(67 citation statements)

References 10 publications

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“…The same is true also in the unfrustrated case. [20,21] This feature can be already observed within the linear spin wave analysis. [29] Dotsenko [30] has also obtained the similar result using the mapping onto the nonlinear σ-model.…”

Section: These Hamiltonians Are Diagonalized Asmentioning

confidence: 57%

“…[1-5] However, it is 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 next-nearest exchange interaction (hereafter called J 1 − J 2 model) [6][7][8][9][10][11][12][13][14][15][16][17][18] and the bilayer Heisenberg model [19][20][21][22][23] have been studied extensively. Both of these models are expected to have the quantum disordered ground state for appropriate parameter regime.…”

Section: Introductionmentioning

confidence: 99%

“…Here µ is the Lagrangian multiplier corrresponding to the constraint (3.16). The order parameters are defined by 20) where ρ is the vector to the nearest neighbour sites and δ to the next nearest sites.…”

Section: Introductionmentioning

confidence: 99%

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Modified Spin Wave Theory of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Hida

1996

J. Phys. Soc. Jpn.

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The ground state of the square lattice bilayer quantum antiferromagnet with nearest and next-nearest neighbour intralayer interaction is studied by means of the modified spin wave method. For weak interlayer coupling, the ground state is found to be always magnetically ordered while the quantum disordered phase appear for large enough interlayer coupling.The properties of the disordered phase vary according to the strength of the frustration.In the regime of weak frustration, the disordered ground state is an almost uncorrelated assembly of interlayer dimers, while in the strongly frustrated regime the quantum spin liquid phase which has considerable Néel type short range order appears. The behavior of the sublattice magnetization and spin-spin correlation length in each phase is discussed.

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Section: These Hamiltonians Are Diagonalized Asmentioning

confidence: 57%

Section: Introductionmentioning

confidence: 99%

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Modified Spin Wave Theory of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Hida

1996

J. Phys. Soc. Jpn.

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“…This quantum criticality could then be realized in layered antiferromagnets doped with non-magnetic impurities. It may already have been observed in La 2 Cu 1−x (Zn,Mg) x O 4 , for which recent neutron scattering experiments [12] show a correlation length divergence roughly consistent with the dynamic exponent z ≈ 1.3 extracted here.The clean S = 1/2 bilayer Heisenberg model has been extensively studied in the past [13,14]. It undergoes a quantum phase transition between an antiferromagnetic and a quantum disordered state as a function of the ratio g = J 2 /J 1 of the inter-and intra-plane couplings.…”

mentioning

confidence: 99%

“…The clean S = 1/2 bilayer Heisenberg model has been extensively studied in the past [13,14]. It undergoes a quantum phase transition between an antiferromagnetic and a quantum disordered state as a function of the ratio g = J 2 /J 1 of the inter-and intra-plane couplings.…”

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confidence: 99%

Multicritical Point in a Diluted Bilayer Heisenberg Quantum Antiferromagnet

Sandvik

2002

Phys. Rev. Lett.

104

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The S = 1/2 Heisenberg bilayer antiferromagnet with randomly removed inter-layer dimers is studied using quantum Monte Carlo simulations. A zero-temperature multi-critical point (p * , g * ) at the classical percolation density p = p * and inter-layer coupling g * ≈ 0.16 is demonstrated. The quantum critical exponents of the percolating cluster are determined using finite-size scaling. It is argued that the associated finite-temperature quantum critical regime extends to zero inter-layer coupling and could be relevant for antiferromagnetic cuprates doped with non-magnetic impurities.PACS numbers: 75.10. Jm, 75.10.Nr, 75.40.Mg, 75.40.Cx Randomly diluted quantum spin systems combine aspects of the percolation problem [1] with the physics of thermal and quantum fluctuations. In systems that can be tuned through a T = 0 phase transition as a function of some parameter one can hence study divergent quantum fluctuations coexisting with classical fluctuations due to percolation. A multi-critical point, where the two types of fluctuations diverge simultaneously, is realized in the transverse Ising model with dimensionality D > 1 [2,3]. In models with O(N ) symmetry and N > 2 such a point was believed not to exist, because quantum fluctuations were argued to always destroy the long-range order on the percolating cluster [3]. Several studies of diluted 2D Heisenberg antiferromagnets were consistent with this scenario [4,5,6]. However, recent quantum Monte Carlo simulations have shown that longrange order in the 2D Heisenberg model persists until the percolation point [7,8,9] and that the percolating cluster is ordered as well [8,9]. This implies that the phase transition is a classical percolation transition. It also suggests that a multi-critical point, at which the percolating cluster is quantum critical, could be reached by including other interactions. In this Letter it will be shown that the O(3) multi-critical point can be realized in the Heisenberg bilayer with dimer dilution, i.e., where adjacent spins on opposite layers are removed together. This system is illustrated in Fig. 1, and a schematic T = 0 phase diagram is shown in Fig. 2. In analogy with quantum critical points in clean 2D Heisenberg antiferromagnets [10,11], one can expect a finite-T universal quantum critical scaling regime to extend to couplings well beyond the T = 0 critical coupling g * , possibly all the way to decoupled layers (g = 0). This quantum criticality could then be realized in layered antiferromagnets doped with non-magnetic impurities. It may already have been observed in La 2 Cu 1−x (Zn,Mg) x O 4 , for which recent neutron scattering experiments [12] show a correlation length divergence roughly consistent with the dynamic exponent z ≈ 1.3 extracted here.The clean S = 1/2 bilayer Heisenberg model has been extensively studied in the past [13,14]. It undergoes a quantum phase transition between an antiferromagnetic and a quantum disordered state as a function of the ratio g = J 2 /J 1 of the inter-and intra-plane couplings. The criti...

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Disordered Ground‐State Properties of the Double‐Layer Antiferromagnetic Quantum XXZ Model

Wei

2001

phys. stat. sol. (b)

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The double-layer antiferromagnetic quantum XXZ model is studied by the bond-operator meanfield theory. The transverse and longitudinal modes in excited spectra, and the phase diagram for disorder-order phase transition about D and J/J ? , which are the relative strength of spin anisotropy and the ratio of the intralayer coupling to the interlayer coupling, respectively, are obtained. It is found that the critical ratio of (J/J ? ) c is 0.174 for XY model (D = 0), and is 0.430 for isotropic model (D = 1). In the disordered phase and on the critical points, the excitation spectra are analyzed. The spin gap from the condensed spin singlets to the first excited states, the ground state energy and the spin wave velocities in the disordered state are calculated as functions of parameters D and J/J ? .

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Low Temperature Properties of the Double Layer Quantum Heisenberg Antiferromagnet -Modified Spin Wave Method-

Cited by 56 publications

References 10 publications

Modified Spin Wave Theory of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Modified Spin Wave Theory of the Bilayer Square Lattice Frustrated Quantum Heisenberg Antiferromagnet

Multicritical Point in a Diluted Bilayer Heisenberg Quantum Antiferromagnet

Disordered Ground‐State Properties of the Double‐Layer Antiferromagnetic Quantum XXZ Model

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