Nature of the 1/9-magnetization plateau in the spin- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mfrac><mml:mn>1</mml:mn><mml:mn>2</mml:mn></mml:mfrac></mml:math> kagome Heisenberg antiferromagnet

The nature of the 1/9-magnetization plateau spin-1/2 kagome Heisenberg antiferromagnet remains controversial due to exotic physical properties and high complexity induced by geometrical frustration. Instead a Z3 quantum spin liquid revealed on cylinder, we show an infinite-size lattice that 1/9 can be described valence bond crystal (VBC) breaks spatial translational invariance. Consistent results are achieved two accurate tensor network methods, namely full-update infinite projected-entangled pair states simplex states. VBC exhibits hourglass pattern with $\sqrt{3}\times\sqrt{3}$ symmetry, demonstrated magnetizations, energies, three-body correlators. inversion symmetry in is instantly broken presence difference between coupling strengths up down triangles, suggesting existence gapless excitations. further indicated scaling behaviors entanglement entropy correlation length, which indicate c=1 conformal field theory.