Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model

Abstract

We apply symmetric tensor network state (TNS) to study the nearest neighbor spin-1/2 antiferromagnetic Heisenberg model on Kagome lattice. Our method keeps track of the global and gauge symmetries in TNS update procedure and in tensor renormalization group (TRG) calculation. 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 Heisenberg model on Kagome lattice is a gapped spin liquid with the ${\mathbb{Z}}_2$-topological order (or toric code type), which has a long correlation length $\xi \sim 10$ unit cell length. We justify that the TRG method can handle very large systems with over thousands of spins. Such a long $\xi$ explains the gapless behaviors observed in simulations on smaller systems with less than 300 spins or shorter than 10 unit cell length. We also discuss experimental implications of the topological excitations encoded in our symmetric tensors.

10 pages, 7 figures

References in corpus (26)

• The density-matrix renormalization group in the age of matrix product states
• A class of quantum many-body states that can be efficiently simulated
• Spin Dynamics of the Spin-1/2 Kagome Lattice Antiferromagnet ZnCu_3(OH)_6Cl_2
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Tensor renormalization group approach to 2D classical lattice models
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Properties of an algebraic spin liquid on the kagome lattice
• Tensor-entanglement renormalization group approach to 2D quantum systems
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Dzyaloshinsky-Moriya Anisotropy in the Spin-1/2 Kagomé Compound ZnCu${}_3$(OH)${}_6$Cl${}_2$
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Resonating valence bond states in the PEPS formalism
• ^{63}Cu, ^{35}Cl, and ^{1}H NMR in the S=1/2 Kagomé Lattice ZnCu_{3}(OH)_{6}Cl_{2}
• Triplet and Singlet Excitations in the Valence Bond Crystal Phase of Kagome Lattice Heisenberg Model
• Constraints on topological order in Mott Insulators
• Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet
• Local Spin Susceptibility of the S=1/2 Kagome Lattice in ZnCu3(OD)6Cl2
• Modular matrices from universal wave function overlaps in Gutzwiller-projected parton wave functions
• Hexagon-singlet solid ansatz for the spin-1 kagome antiferromagnet
• Energy density of variational states
• No-Go Theorem for Boson Condensation in Topologically Ordered Quantum Liquids
• Fractionalized spin-wave continuum in spin liquid states on the kagome lattice

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