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
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