Nature of chiral spin liquids on the kagome lattice

Wietek, Alexander; Sterdyniak, A.; Läuchli, Andreas M.

doi:10.1103/physrevb.92.125122

Cited by 88 publications

(109 citation statements)

References 65 publications

(83 reference statements)

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“…where J φ = cos φ ∝ h. As we previously mentioned, the scalar spin chirality breaks time-reversal (T ) symmetry macroscopically and can be spontaneously developed in CSL [1][2][3][4][5][6][7][8]. Its effects on the magnetic excitations should be the same in the ordered and disordered phases.…”

Section: Topological Magnetic Excitationsmentioning

confidence: 98%

“…But herbertsmithite ZnCu 3 (OH) 6 Cl 2 has D ⊥ /J ∼ 0.08 [30], thus remain a QSL. An applied magnetic field (H ⊥ 2D plane) can induce noncoplanar spin textures with a nonzero scalar spin chirality.…”

Section: Introductionmentioning

confidence: 99%

“…The recent theoretical numerical work shows that a CSL can emerge in a kagomé lattice Mott insulator in which a magnetic field induces an explicit spin chirality interaction in a t/U perturbative expansion of the Hubbard model at half filling [4], hence TRS is broken explicitly. In other numerical works a spontaneously broken TRS CSL is found away from the isotropic kagomé-lattice antiferromagnet by adding additional second and third nearest neighbour interactions [5][6][7][8][9] or Ising anisotropy [10].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

Owerre¹

2017

EPL

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In this Letter, we identify a noncoplanar chiral spin texture on the distorted kagomé-lattice antiferromagnets induced by the presence of a magnetic field applied perpendicular to the distorted kagomé plane. The noncoplanar chiral spin texture has a nonzero scalar spin chirality similar to a chiral quantum spin liquid with broken time-reversal symmetry. In the noncoplanar regime we observe nontrivial topological magnetic excitations and thermal Hall response through the emergent field-induced scalar spin chirality in contrast to collinear ferromagnets in which the DzyaloshinskiiMoriya (DM) spin-orbit interaction is the driving force. Our results shed light on recent observation of thermal Hall conductivity in distorted kagomé volborthite at nonzero magnetic field with no signal of DM spin-orbit interaction, and the results also apply to other distorted kagomé antiferromagnets such as vesignieite and edwardsite.

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Section: Topological Magnetic Excitationsmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

Owerre¹

2017

EPL

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“…The most important one is the Kitaev model on the decorated honeycomb lattice [23], which can be solved exactly by a mapping to Majorana fermions. In addition, strong numerical evidence for a CSL regime has been found in models of broken [25,26] and conserved [27][28][29][30][31] SU (2) spin symmetry on the kagome lattice, where competing magnetic order is sufficiently frustrated. From the viewpoint of symmetry classification, SU(2) symmetry is not a characteristic feature of CSLs.…”

mentioning

confidence: 99%

Coupled-wire construction of chiral spin liquids

et al. 2015

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We develop a coupled wire construction of chiral spin liquids. The starting point are individual wires of electrons in the Mott regime that are subject to a Zeeman field and Rashba spin-orbit coupling. Suitable spin-flip couplings between the wires yield an Abelian chiral spin liquid state which supports spinon excitations above a bulk gap, and chiral edge states. The approach generalizes to non-Abelian chiral spin liquids at level k with parafermionic edge states.PACS numbers: 71.10. Pm, 75.10.Kt, Introduction.-The experimental discovery [1] and conceptual understanding [2] of the fractional quantum Hall effect (FQHE) had a tremendous impact on contemporary research of strongly correlated electron systems. In particular, it triggered interest in topologically ordered quantum states of matter, which since then have persisted as a predominant focus. Following up on an idea by D. H. Lee, Kalmeyer and Laughlin [3,4] proposed the chiral spin liquid [5,6] (CSL) as a fractionally quantized Hall liquid for bosonic spin flip operators acting on a spin-polarized reference state. Fractionalization of charge for FQHE relates to fractionalization of spin for the CSL, which supports S = 1/2 spinons obeying halfFermi statistics [7]. The CSL has been an invaluable seed for new concepts such as topological order [8], providing a direct perspective on the fundamental relations between FQHE, spin liquids, and superconductivity [5,9]. Despite its high relevance as a paradigm formulated via wave functions, the first Hamiltonian for which the CSL is the (aside from topological degeneracies) unique ground state was only identified two decades after the liquid had been proposed [10]. The approach was subsequently expanded to yield different classes of such trial Hamiltonians [11], where the latest and more generic versions are more short-ranged than the initial microscopic models: they involve 2-body and 3-body spin interactions which can be deduced from the explicit construction of appropriate annihilation operators [12] or null operators in conformal field theory [13]. In particular, non-Abelian chiral spin liquids with level k parafermionic spin excitations have been proposed [12,14], which nurture the hope for alternative scenarios of topological quantum computation in frustrated magnets and Mott regimes of alkaline earth atoms deposited in optical lattices [15,16].Since their discovery, CSLs have been appreciated as a realisation of a bosonic Laughlin state at Landau level filling fraction ν = 1/2 on a spin lattice. Naturally, the CSL of Refs. 3 and 4 can be defined on any lattice [17,18], which becomes mathematically transparent via the generalized Perelomov identity [19] for lattices with a primitive unit cell. Some of these motifs have later reappeared in the field of fractional Chern insulators [20][21][22]. As

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“…Several recent investigations have been focused on s > 1/2 [10,[19][20][21][22][23][24][25], anisotropic models [16,[25][26][27][28][29][30][31][32][33][34] as well as KAFMs with further-neighbor couplings [31,[35][36][37][38][39][40][41][42][43][44][45][46][47][48]. It has been found that such modifications of the pure KAFM may play a crucial role either to modify the QSL state or even to establish GS magnetic LRO of √ 3 × √ 3 or of q = 0 symmetry.…”

mentioning

confidence: 99%

The route to magnetic order in the spin-1/2 kagome Heisenberg antiferromagnet: The role of interlayer coupling

Götze¹,

Richter²

2016

EPL

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While the existence of a spin-liquid ground state of the spin-1/2 kagome Heisenberg antiferromagnet (KHAF) is well established, the discussion of the effect of an interlayer coupling (ILC) by controlled theoretical approaches is still lacking. Here we study this problem by using the coupledcluster method to high orders of approximation. We consider a stacked KHAF with a perpendicular ILC J ⊥ , where we study ferro-as well as antiferromagnetic J ⊥ . We find that the spin-liquid ground state (GS) persists until relatively large strengths of the ILC. Only if the strength of the ILC exceeds about 15% of the intralayer coupling the spin-liquid phase gives way for q = 0 magnetic long-range order, where the transition between both phases is continuous and the critical strength of the ILC, |J c ⊥ |, is almost independent of the sign of J ⊥ . Thus, by contrast to the quantum GS selection of the strictly two-dimensional KHAF at large spin s, the ILC leads first to a selection of the q = 0 GS. Only at larger |J ⊥ | the ILC drives a first-order transition to the √ 3 × √ 3 long-range ordered GS. As a result, the stacked spin-1/2 KHAF exhibits a rich GS phase diagram with two continuous and two discontinuous transitions driven by the ILC. Introduction.-The search for exotic quantum spin liquid (QSL) states and fractionalized quasiparticles in frustrated magnets attracts currently much attention both from the theoretical and experimental side. One of the most promising, fascinating, and, at same time, challenging problems is the investigation of the ground state (GS) of the quantum antiferromagnet on the kagome lattice. Over the last 25 years a plethora of theoretical approaches has been applied to understand the GS properties of the spin-1/2 kagome antiferromagnet (KAFM), see, e.g., Refs. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18]. Clearly, the GS of the s = 1/2 Heisenberg KAFM does not exhibit GS magnetic longrange order (LRO). However, there is a long-standing debate on the nature of the quantum GS. Recent largescale numerical studies [6,8,11] provide arguments for a gapped Z 2 topological QSL for spin s = 1/2. However, the gap state is not fully proven, and also a gapless spin liquid is suggested, see, e.g., Refs. [9,12,16].

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Nature of chiral spin liquids on the kagome lattice

Cited by 88 publications

References 65 publications

Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

Topological magnetic excitations on the distorted kagomé antiferromagnets: Applications to volborthite, vesignieite, and edwardsite

Coupled-wire construction of chiral spin liquids

The route to magnetic order in the spin-1/2 kagome Heisenberg antiferromagnet: The role of interlayer coupling

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