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

Tao Liu,1 Wei Li,2,3,* Andreas Weichselbaum,2 Jan von Delft,2 and Gang Su1,†

1Theoretical Condensed Matter Physics and Computational Materials Physics Laboratory, School of Physics, University of Chinese Academy of Sciences, Beijing 100049, China 2Physics Department, Arnold Sommerfeld Center for Theoretical Physics, and Center for NanoScience, Ludwig-Maximilians-Universitat, 80333 Munich, Germany ¨

3Department of Physics, Beihang University, Beijing 100191, China (Received 25 June 2014; revised manuscript received 21 January 2015; published 23 February 2015)

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 = −1.410 90(2), with D∗ = 8 multiplets retained (i.e., a bond dimension of D = 24), and e0 = −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 δ ≈ 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