Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

Abstract

The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.

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References in corpus (20)

• A class of quantum many-body states that can be efficiently simulated
• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• 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
• The iTEBD algorithm beyond unitary evolution
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• Properties of an algebraic spin liquid on the kagome lattice
• A classification of symmetry enriched topological phases with exactly solvable models
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Ground State of the Kagome Lattice Heisenberg Antiferromagnet
• Classifying fractionalization: symmetry classification of gapped Z2 spin liquids in two dimensions
• Resonating valence bond states in the PEPS formalism
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Monte Carlo simulation with Tensor Network States
• Distinct Spin Liquids and their Transitions in Spin-1/2 XXZ Kagome Antiferromagnets
• Variational study of J1-J2 Heisenberg model on Kagome lattice using projected Schwinger boson wave functions
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Detecting crystal symmetry fractionalization from the ground state: Application to ${\mathbb{Z}}_2$ spin liquids on the kagome lattice
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids

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