Planar pyrochlore antiferromagnet: A large-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mi>N</mml:mi></mml:mrow></mml:math>analysis

Bernier, Jean-Sébastien; Chung, Chung-Hou; Kim, Yong Baek; Sachdev, Subir

doi:10.1103/physrevb.69.214427

Cited by 28 publications

(36 citation statements)

References 48 publications

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“…Different from the 1D pyrochlore strip considering in this article, for both the 3D and 2D pyrochlore lattices, each corner of the tetrahedron is shared by a neighboring tetrahedron. As one of the most frustrated antiferromagnets, the model of spin pyrochlore lattice has been investigated by a variety of techniques including the semiclassical large-S limit, large-N expansion of the SU (N ) model, the contractor renormalization method based on the cluster expansion, and the bosonization method on the anisotropic limit 14,15,16,17 . In spite of the intensive research, even the ground state properties of the 3D pyrochlore lattice are not well understood.…”

Section: Introductionmentioning

confidence: 99%

Exact ground state and elementary excitations of the spin tetrahedron chain

et al. 2006

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We study the antiferromagnetic spin exchange models with S = 1/2 and S = 1 on a onedimensional tetrahedron chain by both analytical and numerical approaches. The system is shown to be effectively mapped to a decoupled spin chain in the regime of strong rung coupling, and a spin sawtooth lattice in the regime of weak rung coupling with spin 2S on the top row and spin S on the lower row. The ground state for the homogeneous tetrahedron chain is found to fall into in the regime of strong rung coupling. As a result, the elementary excitation for the spin-1/2 system is gapless whereas the excitation for the spin-1 system has a finite spin gap. With the aid of the exact diagonalization method, we determine the phase diagram numerically and find the existence of an additional phase in the intermediate regime. This phase is doubly degenerate and is characterized by an alternating distribution of rung singlet and rung spin 2S. We also show that the SU (3) exchange model on the same lattice has completely different kind of ground state from that of its SU (2) correspondence and calculate its ground state and elementary excitation analytically.

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Section: Introductionmentioning

confidence: 99%

Exact ground state and elementary excitations of the spin tetrahedron chain

et al. 2006

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“…We also calculated the anharmonic effective Hamiltonian for the (planar) checkerboard lattice, a tractable test-bed for pyrochlore calculations [3,6,26]. But, inescapably, two bonds of every "tetrahedron", (appearing as diagonals of a square) have no symmetry reason to be degenerate with the other four bonds.…”

Section: Effective Hamiltonian Numerical Results and Discussionmentioning

confidence: 99%

“…In the pyrochlore antiferromagnet, there are exponentially many, corresponding to the same collinear states as in the spin-wave expansion and labeled by the same Ising variables {η i }. Prior studies just investigated high symmetry states, or every state in a small finite system [28,26]. We pursue instead the effective Hamiltonian approach.…”

Section: Large-n Approach To Large-s Limitmentioning

confidence: 99%

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Effective Hamiltonians for large-Spyrochlore antiferromagnets

Hizi

Henley

2007

J. Phys.: Condens. Matter

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Abstract. The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground state degeneracy. We summarize three approximation schemes, valid for large spin length S, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuations are taken into account; all three are related to analytic loop expansions. The first is harmonic order spin waves; at this order, there remains an infinite manifold of degenerate collinear ground states, related by a gauge-like symmetry. The second is anharmonic (quartic order) spin waves, using a self-consistent approximation; the harmonic-order degeneracy is split, but (within numerical precision) some degeneracy may remain, with entropy still of order L in a system of L 3 sites. The third is a large-N approximation, a standard and convenient approach for frustrated antiferromagnets; however, the large-N result contradicts the harmonic order at O(S) hence must be wrong (for large S).

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“…So far, the magnetic properties of the checkerboard lattice have been the focus of many theoretical studies, [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19] with P compelling evidence that the ground state for J = J (the planar pyrochlore) is a plaquette valence-bond solid (P-VBS) with long-range quadrumer order. 4,[6][7][8][9][10]12 This was shown by means of strong-coupling expansion, 4,6 exact diagonalization, 7 as well as mean field theory 10 and a quadrumer boson approximation.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics of the antiferromagnetic Heisenberg model on the checkerboard lattice

Khatami

Rigol

2011

Phys. Rev. B

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Employing numerical linked-cluster expansions (NLCEs) along with exact diagonalizations of finite clusters with periodic boundary condition, we study the energy, specific heat, entropy, and various susceptibilities of the antiferromagnetic Heisenberg model on the checkerboard lattice. NLCEs, combined with extrapolation techniques, allow us to access temperatures much lower than those accessible to exact diagonalization and other series expansions. We show that the high-temperature peak in specific heat decreases as the frustration increases, consistent with the large amount of unquenched entropy in the region around maximum classical frustration, where the nearest-neighbor and next-nearest-neighbor exchange interactions (J and J P , respectively) have the same strength, and with the formation of a second peak at lower temperatures. The staggered susceptibility shows a change of character when J P increases beyond 0.75J , implying the disappearance of the antiferromagnetic order P at low temperatures. For J = 4J , in the limit of weakly coupled crossed chains, we find large susceptibilities for stripe and Néel order with Q = (π/2,π/2) at intermediate temperatures. Other magnetic and bond orderings, such as a plaquette valence-bond solid and a crossed-dimer order suggested by previous studies, are also investigated.

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Planar pyrochlore antiferromagnet: A large-Nanalysis

Cited by 28 publications

References 48 publications

Exact ground state and elementary excitations of the spin tetrahedron chain

Exact ground state and elementary excitations of the spin tetrahedron chain

Effective Hamiltonians for large-Spyrochlore antiferromagnets

Thermodynamics of the antiferromagnetic Heisenberg model on the checkerboard lattice

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