2017
DOI: 10.1103/physrevb.95.235107
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Gapped spin liquid with Z2 topological order for the kagome Heisenberg model

Abstract: We apply the symmetric tensor network state (TNS) to study the nearest-neighbor spin-1/2 antiferromagnetic Heisenberg model on the kagome lattice. Our method keeps track of the global and gauge symmetries in the TNS update procedure and in tensor renormalization group (TRG) calculations. We also introduce a very sensitive probe for the gap of the ground state-the modular matrices, which can also determine the topological order if the ground state is gapped. We find that the ground state of the Heisenberg model… Show more

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Cited by 138 publications
(107 citation statements)
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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%
“…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%
“…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%
“…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%