Planar pyrochlore: A valence-bond crystal

Fouet, J.-B.; Mambrini, Matthieu; Sindzingre, Philippe; Lhuillier, C.

doi:10.1103/physrevb.67.054411

Cited by 120 publications

(207 citation statements)

References 34 publications

(45 reference statements)

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“…These include studies on the honeycomb lattice [66] (duality mapping on the honyecomb lattice appears in Ref. [19]), on the planar pyrochlore lattice [67,68] (duality mapping for a lattice with the symmetry of the planar pyrochore is in Refs. [69,64], with a prediction for the bond order observed), on square lattice models with ring-exchange and easy-plane spin symmetry [70] (duality mapping on spin models with easy plane symmetry is in Refs.…”

Section: S Half-odd-integermentioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

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Summary. This article contains a theoretical overview of the physical properties of antiferromagnetic Mott insulators in spatial dimensions greater than one. Many such materials have been experimentally studied in the past decade and a half, and we make contact with these studies. The simplest class of Mott insulators have an even number of S = 1/2 spins per unit cell, and these can be described with quantitative accuracy by the bond operator method: we discuss their spin gap and magnetically ordered states, and the transitions between them driven by pressure or an applied magnetic field. The case of an odd number of S = 1/2 spins per unit cell is more subtle: here the spin gap state can spontaneously develop bond order (so the ground state again has an even number of S = 1/2 spins per unit cell), and/or acquire topological order and fractionalized excitations. We describe the conditions under which such spin gap states can form, and survey recent theories (T. Senthil et al., cond-mat/0312617) of the quantum phase transitions among these states and magnetically ordered states. We describe the breakdown of the Landau-GinzburgWilson paradigm at these quantum critical points, accompanied by the appearance of emergent gauge excitations.

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Section: S Half-odd-integermentioning

confidence: 99%

Quantum phases and phase transitions of Mott insulators

Sachdev

2004

Quantum Magnetism

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“…On the 2(3) × 2 · 4 lattice we observe a kink in the e g (j) as obtained from the ED at j ≈ 1 which suggests a change of the nature of the ground state on these systems in the vicinity of j = 1. This is probably a special property of the 16(24)-spin lattices 6 .…”

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confidence: 99%

“…In particular, ED at j = 1 has resulted in a sizeable spin gap and a large number of in-gap singlet states 3,6 . Moreover, recent ED 6 has given strong evidence in favor of a valence bond crystal (VBC) ground state with long range order in the S = 0 quadrumers shown in Fig.…”

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Planar pyrochlore: A strong-coupling analysis

Brenig

Honecker

2002

Phys. Rev. B

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Recent investigations of the two-dimensional spin-1/2 checkerboard lattice favor a valence bond crystal with long range quadrumer order [J.-B. Fouet et al., preprint cond-mat/0108070]. Starting from the limit of isolated quadrumers, we perform a complementary analysis of the evolution of the spectrum as a function of the inter quadrumer coupling j using both, exact diagonalization (ED) and series expansion (SE) by continuous unitary transformation. We compute (i) the ground state energy, (ii) the elementary triplet excitations, (iii) singlet excitations on finite systems and find very good agreement between SE and ED. In the thermodynamic limit we find a ground state energy substantially lower than documented in the literature. The elementary triplet excitation is shown to be gapped and almost dispersionless, whereas the singlet sector contains strongly dispersive modes. Evidence is presented for the low energy singlet excitations in the spin gap in the vicinity of j = 1 to result from a large downward renormalization of local high-energy states. Quantum-magnetism in low dimensions has received considerable attention recently due to the discovery of numerous materials with spin-1/2 moments arranged in chain, ladder, and depleted planar structures. Many of these systems exhibit strongly gapped excitation spectra induced by various types of magnetic dimerization and discrete symmetry breakings. Yet, low energy collective spin dynamics may emerge from materials with strong geometrical frustration leading to ground states with near macroscopic degeneracy and possibly even zero temperature entropy 1,2 . In this respect quantum spin systems on the kagomé, and more recently on the pyrochlore lattice are of particular interest. While their classical counterparts have been studied in considerable detail the role of quantum fluctuations in such systems is an open issue. For the spin-1/2 kagomé lattice gapless singlet excitations and a high density of singlet states in the singlettriplet gap have been established on finite systems by ED 2 . Similar analysis of the pyrochlore quantum-magnet is severely constrained by its three-dimensional structure. Therefore, and as a first step, several investigations 3,4,5,6 have focussed on the planar projection of the pyrochlore quantum-magnet, i.e. the spin-1/2 checkerboard lattice of Fig. 1a) for the case of j = 1.In particular, ED at j = 1 has resulted in a sizeable spin gap and a large number of in-gap singlet states 3,6 . Moreover, recent ED 6 has given strong evidence in favor of a valence bond crystal (VBC) ground state with long range order in the S = 0 quadrumers shown in Fig. 1a). While this has been concluded from the quadrumer correlation at j = 1 it emphasizes the need for a perturbative investigation of the checkerboard magnet starting from the limit j → 0 in Fig. 1a). Low-order perturbation theory has been performed previously for the checkerboard magnet 4 however with the unperturbed Hamiltonian chosen at variance with the VBC found in the ED 6 . Therefore, the purpose ...

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“…Besides the checkerboard lattice, 12 we have found a VBC phase in the J 1 −J 2 model on the honeycomb lattice. 8 In these three systems the VBC phase is located in the phase diagram near a collinear Néel phase.…”

Section: Vbc Lromentioning

confidence: 96%