Physics 682
Topics in Condensed Matter Theory:
Quantum Magnetism
Spring 2004
Suggested presentation topics

Topological versus "spinwave" transitions in
statistical mechanics.
XY and Ising models, classical
Hesenberg model in three dimensions.
B. I. Halperin, in Physics of defects ,
Proceedings of the Les Houches
Summer Institute (NorthHolland, Amsterdam 1980).
Mh. Lau, C. Dasgupta, Phys. Rev. B, 39,
7212 (1989)
Numerical investigation of the role of topological defects in the
threedimensional Heisenberg transition.
M. Kamal, G. Murthy, Phys. Rev. Lett., 71,
1911 (1993)
New O(3) Transition in Three Dimensions.
O. I. Motrunich, A. Vishwanath, condmat/0311222 (2003)
Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression.

Quantum phase transitions (e.g. in transverse field Ising).
Subir Sachdev,
Cambridge University Press, 1999.
Quantum Phase Transitions,

Geometric phase associated with instantons for twodimensional quantum
Heisenberg model.
F. D. M. Haldane, Phys. Rev. Lett., 61,
10291032 (1988).
O(3) Nonlinear SigmaModel and the Topological
Distinction between Integer and HalfIntegerSpin
Antiferromagnets in 2 Dimensions.
S. Sachdev and N. Read, Int. J. Mod. Phys. B, 5,
219249 (1991).
Large N Expansion for Frustrated and Doped
Quantum Antiferromagnets.

Spin gap phase in CaV_{4}O_{9}.
O.A. Starykh et. al., Phys. Rev. Lett,
77, 2558
(1996).
Origin of Spin Gap in CaV_{4}O_{9}: Effects of Frustration
and Lattice Distortions.
S. Taniguchi et al., J. Phys. Soc. Jpn.
64, 2758 (1995).
Spin Gap Behavior of S=1/2 QuasiTwoDimensional System
CaV_{4}O_{9}.

Spinons versus magnons. O(N) versus CP^{M1}
approach to spin models.
A.V. Chubukov and O.A. Starykh, Phys. Rev. B,
52, 440
(1995).
Confinement of spinons in CP^{M1} model.

KalmeyerLaughlin state of two dimensional antiferromagnets.
V. Kalmeyer and R.B. Laughlin, Phys. Rev. B,
39,
11879 (1989).
Theory of the spin liquid state of the Heisenber antiferromagnet.

Dimerized versus Haldane phase of spin ladder.
A.O. Gogolin, A.A. Nersesyan, A.M. Tsvelik,
Cambridge University Press, 1998, Ch. 21.
Bosonization and Strongly Correlated Systems,

Topological order. Boundary states of spin chains (experiment).
M. Hagiwara et. al., Physica B, 177, 386
(1992).
Magnetization process of an S=1 impure linear chain Heisenberg
antiferromagnet.

RVB and Quantum Dimer models.
S.A. Kivelson, D.S. Rokhsar, and J.P. Sethna, Phys. Rev. B
35, 8865 (1987).
Topology of the resonating valencebond state:
Solitons and highTc superconductivity.
R. Moessner and S.L. Sondhi, Phys. Rev. Lett.
86, 1881 (2001).
Resonating Valence Bond Phase in the Triangular
Lattice Quantum Dimer Model.