Gapped spin liquid with 
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 topological order for the kagome Heisenberg model

Mei, Jia-Wei; Chen, Jiyao; He, Huan; Wen, Xiao-Gang

doi:10.1103/physrevb.95.235107

Cited by 135 publications

(107 citation statements)

References 103 publications

(186 reference statements)

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“…52 suggested the spin-1/2 Heisenberg model on Kagome lattice to be gapped, but the details of the results are inconsistent with Z 2 -topological order, which led people to suspect that the model is gapless. A more recent numerical calculation suggests the model to have a Z 2 -topological order with long correlation length (10 unit cell length) [53], while several other calculations suggest gapless U (1) spin liquid ground states [54][55][56].…”

Section: String Liquid In Spin Liquid: Emergence Of Gauge Theorymentioning

confidence: 99%

Choreographed entanglement dances: Topological states of quantum matter

Wen

2019

Science

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For a long time, we thought that only symmetry breaking can give rise to different phases of matter. If there was no symmetry breaking, there would be no pattern and it would be featureless. But now we realize that, for quantum matter at zero temperature, even symmetric disordered liquids can have features, which give rise to topological phases of quantum matter. Some of the topological phases are highly entangled (i.e. have topological order), while others are weakly entangled (i.e. have SPT order). In this article, we will briefly introduce those new zero-temperature states of matter and their amazing emergent properties. We will also discuss their significance in unifying some most basic concepts in nature. :1906.05983v1 [cond-mat.str-el] CONTENTS arXiv

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Section: String Liquid In Spin Liquid: Emergence Of Gauge Theorymentioning

confidence: 99%

Choreographed entanglement dances: Topological states of quantum matter

Wen

2019

Science

Self Cite

161

128

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“…However, the precise nature of this spin liquid is still actively debated. While the HLSM theorem [8] excludes a unique GS separated from the first excitations by a finite gap (so-called "trivial" spin liquid), a gapless spin liquid [9][10][11][12] or a gapful topological spin liquid (of the RVB type) [13][14][15] are the two favored candidates.…”

Section: Introductionmentioning

confidence: 99%

Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

2020

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We investigate the spin-1/2 Heisenberg antiferromagnet on the kagome lattice with breathing anisotropy (i.e. with weak and strong triangular units), constructing an improved simplex Resonating Valence Bond (RVB) ansatz by successive applications (up to three times) of local quantum gates which implement a filtering operation on the bare nearest-neighbor RVB state. The resulting Projected Entangled Pair State involves a small number of variational parameters (only one at each level of application) and preserves full lattice and spin-rotation symmetries. Despite its simple analytic form, the simplex RVB provides very good variational energies at strong and even intermediate breathing anisotropy. We show that it carries Z2 topological order which does not fade away under the first few applications of the quantum gates, suggesting that the RVB topological spin liquid becomes a competing ground state candidate for the kagome antiferromagnet at large breathing anisotropy.

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“…Some analytical and numerical approaches have predicted a spin liquid ground state for the S=1/2 Heisenberg KA model Hamiltonian with a gapped excitation spectrum. These include studies using exact diagonalization (ED) [4], density-matrix-renormalization group (DMRG) [5][6][7][8][9], quantum Monte Carlo (QMC) [10], Schwinger fermion mean-field method [11], slave fermion approach [12] and tensor network states (TNS) [13,14]. On the other hand, some other studies predict a gapless or critical spin liquid ground state.…”

Section: Introductionmentioning

confidence: 99%

Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis

2019

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We analyze the antiferromagnetic spin-1/2 XXZ model on the kagome lattice at finite external magnetic field with the help of a non-perturbative zero-temperature renormalization group (RG) technique. The exact nature of the ground and excited state properties (e.g. gapped or gapless spectrum etc) of this system are still debated. Approximate methods have typically been adopted towards understanding the low-energy spectrum. Following the work of Kumar et al (2014 Phys. Rev. B 90 174409), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbor interactions. While the work of Kumar et al was confined mostly to the plateau at 1/3-filling (magnetization per site) in the XY regime, we analyze the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel-Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a SU(2)-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar et al. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses. projected wave function based study [15], effective field theories [15, 16], variational QMC analyses [17-19], numerical calculations of quantum dimer models [20] as well as TNS [21, 22], ED [23] and DMRG [24] based studies.Encouragingly, the material Herbertsmithite (ZnCu 3 (OH) 6 Cl 2 ) can be mapped to the n.n. S=1/2 KA model. Here too, however, conclusive results have remained elusive thus far: some experimental results on this material appear to show the existence of gapless excitations [25,26], while some others suggest a gapped spin liquid ground state with fractional excitations [27,28]. The materials Volborthite and Vesignieite [29][30][31][32], as well as the organic compound Cu-titmb [33], are also believed to be described by the S=1/2 Heisenberg KA. Further, in the presence of an external magnetic field, frustrated antiferromagnetic spin systems sometimes display the phenomenon of magnetization plateaux [30,[34][35][36][37]. For ...

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Gapped spin liquid with Z2 topological order for the kagome Heisenberg model

Cited by 135 publications

References 103 publications

Choreographed entanglement dances: Topological states of quantum matter

Choreographed entanglement dances: Topological states of quantum matter

Gapped Z2 spin liquid in the breathing kagome Heisenberg antiferromagnet

Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalization group analysis

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