Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

Cepas, Olivier; Fong, Manson Cheuk-Man; Leung, Pak Wo; Lhuillier, C.

doi:10.1103/physrevb.78.140405

Cited by 215 publications

(287 citation statements)

References 35 publications

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“…Although there are extensive DMRG results, studies of models other than the ideal near neighbor Heisenberg model on the kagome lattice are still in their infancy, even before mentioning PEPS, MERA or quantum Monte Carlo. Various theory papers have pointed to the importance of longer range exchange, DM and anisotropic exchange, and interlayer interactions (Cepas et al, 2008;Jeschke et al, 2013). And the incorporation of defects into theoretical models has only seen limited attention.…”

Section: B Topological Degeneracy and Fractionalized Excitationsmentioning

confidence: 99%

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Colloquium : Herbertsmithite and the search for the quantum spin liquid

2016

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Quantum spin liquids form a novel class of matter where, despite the existence of strong exchange interactions, spins do not order down to the lowest measured temperature. Typically, these occur in lattices that act to frustrate the appearance of magnetism. In two dimensions, the classic example is the kagome lattice composed of corner sharing triangles. There are a variety of minerals whose transition metal ions form such a lattice. Hence, a number of them have been studied, and were then subsequently synthesized in order to obtain more pristine samples. Of particular note was the report in 2005 by Dan Nocera's group of the synthesis of herbertsmithite, composed of a lattice of copper ions sitting on a kagome lattice, which indeed does not order down to the lowest measured temperature despite the existence of a large exchange interaction of 17 meV. Over the past decade, this material has been extensively studied, yielding a number of intriguing surprises that have in turn motivated a resurgence of interest in the theoretical study of the spin 1 2 Heisenberg model on a kagome lattice. In this colloquium article, I will review these developments, and then discuss potential future directions, both experimental and theoretical, as well as the challenge of doping these materials with the hope that this could lead to the discovery of novel topological and superconducting phases.

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Section: B Topological Degeneracy and Fractionalized Excitationsmentioning

confidence: 99%

“…Finally, several studies have shown how the DM term changes the nature of the phase diagram from that shown in Fig. 4, in some cases leading to a stabilization of the liquid phase (Cepas et al, 2008;Elhajal et al, 2002).…”

Section: F Dmrg Peps and Meramentioning

confidence: 99%

Colloquium : Herbertsmithite and the search for the quantum spin liquid

2016

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“…48 It is tempting to speculate that a somewhat similar transition may occur in the S = 1/2 Heisenberg model on kagome with a DM coupling. While the existence of the transition is not in doubt-at a large enough D the system should develop magnetic order [29][30][31][32] -the nature of the transition remains to be determined.…”

Section: Discussionmentioning

confidence: 99%

“…Tovar et al 28 concluded that a finite DM term could be responsible for the non-zero susceptibility observed in experiment even if the spin gap remains finite. A study employing exact diagonalization 29 showed that a sufficiently strong DM term, D > D c ≈ 0.10J, induces long-range magnetic order in the ground state, with magnetic moments lying in the plane. This was later confirmed by employing the Schwinger-boson approach.…”

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confidence: 99%

Destruction of valence-bond order in aS=12sawtooth chain with a Dzyaloshinskii-Moriya term

et al. 2011

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A small value of the spin gap in quantum antiferromagnets with strong frustration makes them susceptible to nominally small deviations from the ideal Heisenberg model. One of such perturbations, the anisotropic Dzyaloshinskii-Moriya interaction, is an important perturbation for the S = 1/2 kagome antiferromagnet, one of the current candidates for a quantum-disordered ground state. We study the influence of the DM term in a related one-dimensional system, the sawtooth chain that has valence-bond order in its ground state. Through a combination of analytical and numerical methods, we show that a relatively weak DM coupling, 0.115J, is sufficient to destroy the valence-bond order, close the spin gap, and turn the system into a Luttinger liquid with algebraic spin correlations. A similar mechanism may be at work in the kagome antiferromagnet.

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“…However, substitutional impurities and Dzyaloshinskii-Moria anisotropy are present in these systems and may be playing a role in producing the eventual thermodynamic phase. 14,15 One Kagome material that does show gapped spinexcitations is Rb 2 Cu 3 SnF 12 . 16,17 This material also has substantial pinwheel distortions, which results in a 12-site unit cell 9 and four different nearest-neighbor exchange constants, with the ratio of the largest to smallest being about two (see Fig.…”

Section: Introductionmentioning

confidence: 99%

Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

2011

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We study the Heisenberg model on the pinwheel distorted Kagome lattice as observed in the material Rb2Cu3SnF12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based zerotemperature numerical linked-cluster expansion to study the approach of the pinwheel distorted lattice to the uniform Kagome lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the Kagome lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel dimerizing perturbations.

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Quantum phase transition induced by Dzyaloshinskii-Moriya interactions in the kagome antiferromagnet

Cited by 215 publications

References 35 publications

Colloquium : Herbertsmithite and the search for the quantum spin liquid

Colloquium : Herbertsmithite and the search for the quantum spin liquid

Destruction of valence-bond order in aS=12sawtooth chain with a Dzyaloshinskii-Moriya term

Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

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