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arXiv · 1406.5905

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

Tao Liu·Wei Li·Andreas Weichselbaum·Jan von Delft·Gang Su
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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 $D^*=8$ 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.

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Tao Liu, Wei Li, Andreas Weichselbaum, Jan von Delft, Gang Su. 2014-06-23. Simplex valence-bond crystal in the spin-1 kagome Heisenberg antiferromagnet. https://doi.org/10.1103/physrevb.91.060403

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