Magnetization curve of the Shastry-Sutherland model

Magnetization curve of the Shastry-Sutherland model

Andreas Honecker1,2, Philippe Corboz3, Salvatore Manmana1, Frédéric Mila4

1 Institut für Theoretische Physik, Georg-August-Universität Göttingen, Germany2 Fakultät für Mathematik und Informatik, Georg-August-Universität Göttingen, Germany

3 Institute for Theoretical Physics, ETH Zürich, Switzerland4 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 1J’/J

0.75

1

1.25

1.5

1.75

2

H/J

N=24N=24aN=36iPEPS, extrapolated

0 0.2 0.4 0.6 0.8 1J’/J

1

1.5

2

2.5

3

H/J

N=16N=24N=24aN=32N=36N=40iPEPS, extrapolated

boundaries of M=⅓ plateau for S=½spin 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

SrCu2(BO3)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 1J’/J

0

1

2

3

4

H/J

M=⅓M=½

SrCu2(BO3)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) 12404Cu, O, B, Sr

⇒ M=⅓ & M=½ plateaux observed

comparison with MERA

0 0.5 1 1.5 2 2.5 3H/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 = 0.635iPEPS

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

saturatedferromagnet

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 ↑↑↓-stateclassical 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

kx

ky

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

acknowledgmentsSPINPACK version 2.43 by Jörg Schulenburg

Shastry-Sutherland model

Hamiltonian:

exchange constant J for dimers and square-lattice coupling Jʻ

H =�

�i,j�

Ji,j�Si ·

�Sj

−H

�

i

Szi