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arXiv:1406.5905 · Physical Review B

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

Tao Liu, Wei Li, Andreas Weichselbaum, Jan von Delft, Gang Su

Published Feb 23, 2015• 56 citations
arXivHTMLPDF

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 ${e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)$, with ${D}^{*}=8$ multiplets retained (i.e., a bond dimension of $D=24)$, and ${e}_{0}=\ensuremath{-}1.4116(4)$ 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 $\ensuremath{\delta}\ensuremath{\approx}19%$, 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 to be a simplex valence-bond crystal. 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.

DOI
10.1103/physrevb.91.060403

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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 e0=\ensuremath−1.41090(2){e}_{0}=\ensuremath{-}1.410\phantom{\rule{0.16em}{0ex}}90(2)e0​=\ensuremath−1.41090(2), with D∗=8{D}^{*}=8D∗=8 multiplets retained (i.e., a bond dimension of D=24)D=24)D=24), and e0=\ensuremath−1.4116(4){e}_{0}=\ensuremath{-}1.4116(4)e0​=\ensuremath−1.4116(4) from large-DDD 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 \ensuremathδ\ensuremath≈19\ensuremath{\delta}\ensuremath{\approx}19%\ensuremathδ\ensuremath≈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 to be a simplex valence-bond crystal. 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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