Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet

Abstract

We investigate the ground state properties of a spin-1 kagome antiferromagnetic Heisenberg model using tensor-network (TN) methods. We obtain the energy per site {$e_0=-1.41090(2)$ with $D^{\ast }=8$ multiplets retained (i.e., a bond dimension of $D=24$), and $e_0=-1.4116(4)$ from large-$D$ extrapolation,} by accurate TN calculations directly in the thermodynamic limit. The symmetry between the two kinds of triangles is spontaneously broken, with a relative energy difference of $\delta \approx$ 19\%, i.e, there is a trimerization (simplex) valence-bond order in the ground state. The spin-spin, dimer-dimer, and chirality-chirality correlation functions are found to decay exponentially with a rather short correlation length, showing that the ground state is gapped. We thus identify the ground state be a simplex valence-bond crystal (SVBC). We also discuss the spin-1 bilinear-biquadratic Heisenberg model on a kagome lattice, and determine its ground state phase diagram. Moreover, we implement non-abelian symmetries, here spin SU(2), in the TN algorithm, which improves the efficiency greatly and provides insight into the tensor structures.

published version

References in corpus (9)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Identifying Topological Order by Entanglement Entropy
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• The iTEBD algorithm beyond unitary evolution
• The quadrupolar phases of the S=1 bilinear-biquadratic Heisenberg model on the triangular lattice
• Efficient simulation of infinite tree tensor network states on the Bethe lattice
• Simplex solids in SU(N) Heisenberg models on the kagome and checkerboard lattices
• Simplex solid states of SU(N) quantum antiferromagnets
• Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field

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• Response to comment on "Spin-lattice coupling and the emergence of the trimerized phase in the $S=1$ kagome antiferromagnet Na${}_2$Ti${}_3$Cl${}_8$", Phys. Rev. Lett. 124, 167203 (2020)