Physics 682
Topics in Condensed Matter Theory:
Quantum Magnetism
Spring 2001

Presentation topics

• Topological versus "spin-wave" 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 (North-Holland, Amsterdam 1980).
  
  M-h. Lau, C. Dasgupta, Phys. Rev. B, 39, 7212 (1989)
  Numerical investigation of the role of topological defects in the three-dimensional Heisenberg transition.
  
  M. Kamal, G. Murthy, Phys. Rev. Lett., 71, 1911 (1993)
  New O(3) Transition in Three Dimensions.
  
  
  
• Geometric phase associated with instantons for two-dimensional quantum Heisenberg model.
  
  F. D. M. Haldane, Phys. Rev. Lett., 61, 1029-1032 (1988).
  O(3) Nonlinear Sigma-Model and the Topological Distinction between Integer and Half-Integer-Spin Antiferromagnets in 2 Dimensions.
  
  S. Sachdev and N. Read, Int. J. Mod. Phys. B, 5, 219-249 (1991).
  Large N Expansion for Frustrated and Doped Quantum Antiferromagnets.
  
  
  
• Spin gap phase in CaV₄O₉.
  
  O.A. Starykh et. al., Phys. Rev. Lett, 77, 2558 (1996).
  Origin of Spin Gap in CaV₄O₉: Effects of Frustration and Lattice Distortions.
  
  S. Taniguchi et al., J. Phys. Soc. Jpn. 64, 2758 (1995).
  Spin Gap Behavior of S=1/2 Quasi-Two-Dimensional System CaV₄O₉.
  
  
  
• Spinons versus magnons. O(N) versus CP^M-1 approach to spin models.
  
  A.V. Chubukov and O.A. Starykh, Phys. Rev. B, 52, 440 (1995).
  Confinement of spinons in CP^M-1 model.
  
  
  
• Kalmeyer-Laughlin 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 valence-bond state: Solitons and high-Tc superconductivity.
  
  R. Moessner and S.L. Sondhi, Phys. Rev. Lett. 86, 1881 (2001).
  Resonating Valence Bond Phase in the Triangular Lattice Quantum Dimer Model.