Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

Gong, Shou-Shu; Zhu, Wei; Balents, Leon; Sheng, D. N.

doi:10.1103/physrevb.91.075112

Cited by 164 publications

(203 citation statements)

References 83 publications

(113 reference statements)

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“…In Ref. [58], a DMRG study of the phase diagram of the J 1 -J 2 -J 3 Heisenberg model on the kagome lattice is performed, and in Ref. [59], the phase diagram of the J 1 -J 2 Heisenberg model on the kagome lattice is studied with a variational Monte Carlo method.…”

Section: Discussionmentioning

confidence: 99%

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

et al. 2015

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We perform an extensive density-matrix renormalization-group study of the ground-state phase diagram of the spin-1/2 J 1 -J 2 Heisenberg model on the kagome lattice. We focus on the region of the phase diagram around the kagome Heisenberg antiferromagnet, i.e., at J 2 = 0. We investigate the static spin structure factor, the magnetic correlation lengths, and the spin gaps. Our results are consistent with the absence of magnetic order in a narrow region around J 2 ≈ 0, although strong finite-size effects do not allow us to accurately determine the phase boundaries. This result is in agreement with the presence of an extended spin-liquid region, as it has been proposed recently. Outside the disordered region, we find that for ferromagnetic and antiferromagnetic J 2 , the ground state displays signatures of the magnetic order of the √ 3 × √ 3 and the q = 0 type, respectively. Finally, we focus on the structure of the entanglement spectrum (ES) in the q = 0 ordered phase. We discuss the importance of the choice of the bipartition on the finite-size structure of the ES.

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Section: Discussionmentioning

confidence: 99%

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

et al. 2015

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“…Most importantly, it is the hallmark of chiral QSLs in which TRS is broken macroscopically without any LRO, that is S j = 0 [39][40][41][42]. The cuboc1 phase on the frustrated kagomé lattice also has a finite scalar spin chirality even in the absence of an explicit DMI [50]. The main origin of the scalar spin chirality is geometrical spin frustration.…”

Section: Arxiv:160804561v12 [Cond-matstr-el] 16 Jan 2017mentioning

confidence: 99%

Topological thermal Hall effect in frustrated kagome antiferromagnets

Owerre

2017

Phys. Rev. B

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In frustrated magnets the Dzyaloshinsky-Moriya interaction (DMI) arising from spin-orbit coupling (SOC) can induce a magnetic long-range order. Here, we report a theoretical prediction of thermal Hall effect in frustrated kagomé magnets such as KCr3(OH)6(SO4)2 and KFe3(OH)6(SO4)2. The thermal Hall effects in these materials are induced by scalar spin chirality as opposed to DMI in previous studies. The scalar spin chirality originates from magnetic-field-induced chiral spin configuration due to non-coplanar spin textures, but in general it can be spontaneously developed as a macroscopic order parameter in chiral quantum spin liquids. Therefore, we infer that there is a possibility of thermal Hall effect in frustrated kagomé magnets such as herbertsmithite ZnCu3(OH)6Cl2 and the chromium compound Ca10Cr7O28, although they also show evidence of magnetic long-range order in the presence of applied magnetic field or pressure.Introduction-. Topological phases of matter are an active research field in condensed matter physics, mostly dominated by electronic systems. Quite recently the concepts of topological matter have been extended to nonelectronic bosonic systems such as quantized spin waves (magnons) [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17] and quantized lattice vibrations (phonons) [18][19][20][21][22][23]. In the former, spin-orbit coupling manifests in the form of Dzyaloshinsky-Moriya interaction [24,25] and it leads to topological spin excitations and chiral edge modes in collinear ferromagnets [5,6]. The quantized spin waves or magnons are charge-neutral quasiparticles and they do not experience a Lorentz force as in charge particles. However, a temperature gradient can induce a heat current and the DMI-induced Berry curvature acts as an effective magnetic field in momentum space. This leads to a thermal version of the Hall effect characterized by a temperature dependent thermal Hall conductivity [1,3]. Thermal Hall effect is now an emerging active research area for probing the topological nature of magnetic spin excitations in quantum magnets. The thermal Hall effect of spin waves has been realized experimentally in a number of pyrochlore ferromagnets [2,4]. Recently, DMI-induced topological magnon bands and thermal Hall effect have been observed in collinear kagomé ferromagnet Cu(1-3, bdc) [8,9].In frustrated kagomé magnets, however, there is no magnetic long-range order (LRO) down to the lowest accessible temperatures. The classical ground states have an extensive degeneracy and they are considered as candidates for quantum spin liquid (QSL) [26,27]. The ground state of spin-1/2 Heisenberg model on the kagomé lattice is believed to be a U(1)-Dirac spin liquid [28]. In physical realistic materials, however, there are other interactions and perturbations that tend to alleviate QSL ground states and lead to LRO. Recent experimental syntheses of kagomé antiferromagnetic materials have shown that the effects of SOC or DMI are not negligible in frustrated magnets. The DMI is an intrinsic pertur...

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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.…”

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confidence: 99%

“…II. The price we pay for the simplicity of the construction is that the Zeeman and spin-orbit couplings violate SU(2) spin symmetry at the single wire level, which is intact in the KL liquid, but not a required property for the universality class of CSLs [23,30].…”

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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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Global phase diagram of competing ordered and quantum spin-liquid phases on the kagome lattice

Cited by 164 publications

References 83 publications

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

Phase diagram of theJ1−J2Heisenberg model on the kagome lattice

Topological thermal Hall effect in frustrated kagome antiferromagnets

Coupled-wire construction of chiral spin liquids

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