Magnetization curve of the Shastry-Sutherland model Andreas Honecker 1,2 , Philippe Corboz 3 , Salvatore Manmana 1 , Frédéric Mila 4 1 Institut für Theoretische Physik, Georg-August-Universität Göttingen, Germany 2 Fakultät für Mathematik und Informatik, Georg-August-Universität Göttingen, Germany 3 Institute for Theoretical Physics, ETH Zürich, Switzerland 4 Institute of Theoretical Physics, EPFL Lausanne, Switzerland FLAT2013, 6-9 March 2013 boundaries of M =½ plateau for S =½ 0 0.2 0.4 0.6 0.8 1 J’/J 0.75 1 1.25 1.5 1.75 2 H/J N=24 N=24a N=36 iPEPS, extrapolated 0 0.2 0.4 0.6 0.8 1 J’/J 1 1.5 2 2.5 3 H/J N=16 N=24 N=24a N=32 N=36 N=40 iPEPS, extrapolated boundaries of M =⅓ plateau for S =½ spin S =½ ☞ exact diagonalization for different N ☞ iPEPS for N=∞ ⇒ M=½ plateau closes at Jʻ/J ≈ 0.68 ⇒ M=⅓ plateau persists up to Jʻ/J ≈ 0.8 phase diagram in a magnetic field M=1 M=0 SrCu 2 (BO 3 ) 2 further plateaux further plateaux (?) 0 1 2 3 4 5 6 7 0 1 2 3 4 5 6 7 6x6, D=6, h=0.8, m=0.33333 0 0.5 1 1.5 2 2.5 3 0 0.5 1 1.5 2 2.5 3 2x2, D=8, h=1.6, m=0.5 0 0.2 0.4 0.6 0.8 1 J’/J 0 1 2 3 4 H/J M=⅓ M=½ SrCu 2 (BO 3 ) 2 structure of a layer high-field magnetization high-field magnetostriction K. Onizuka et al., J. Phys. Soc. Jpn. 69 (2000) 1016 M. Jaime et al., PNAS 109 (2012) 12404 Cu, O , B, Sr ⇒ M=⅓ & M=½ plateaux observed comparison with MERA 0 0.5 1 1.5 2 2.5 3 H/J 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 M/M s ,|S + | M |S + | Jʻ/J = 0.635 iPEPS iPEPS Jie Lou et al., arXiv:1212.1999 ☞ MERA probably overestimates stability of M=½ plateau S =½: almost localized „triplon“ excitations H/J J’/J 0.5 dimer singlets large sublattice structure large sublattice structure saturated ferromagnet 0 1 m = 1/3 m = 1/2 2 perturbation theory in Jʻ/J: ☞ dimer „triplon“ particles ☞ triplon-triplon repulsions dominate over hopping ⇒ crystalline states favored ⇒ plateaux T. Momoi, K. Totsuka, Phys. Rev. B 62 (2000) 15067 S =∞: order-by-disorder stabilization of ↑↑ ↓ -state classical spectrum 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 -π 0 π -2π -π 0 π 2π k x k y classical ↑↑↓-state Jʻ/J = ½: ☞ degeneracy at M=⅓ ☞ ↑↑↓-state: lines of soft modes ⇒ stabilization of M=⅓ pseudo-„plateau“ by fluctuations M. Moliner, D.C. Cabra, A. Honecker, P. Pujol, F. Stauffer, Phys. Rev. B 79 (2009) 144401 acknowledgments SPINPACK version 2.43 by Jörg Schulenburg Shastry-Sutherland model Hamiltonian: exchange constant J for dimers and square- lattice coupling Jʻ H = i,j J i,j S i · S j −H i S z i