Physics 680-04
Special Topics in Condensed Matter Theory:
Topological terms in condensed matter physics
Spring 2009

Suggested presentation topics
(Under construction)

• Media with Non-Abelian fundamental group. Biaxial nematics. (Michael Assis)
  
  N. D. Mermin, Rev. Mod. Phys., 51, 591 (1979).
  The topological theory of defects in ordered media, (PDF, subscription required )
  
  
  
• Polyakov-t'Hooft monopole. (Savvas Zafiropoulos)
  
  R. Rajaraman, Solitons and Instantons, North Holland (1987).
  (Amazon)
  
  
  
• BKT phase transition in XY model. (Yan Xu)
  
  P. M. Chaikin and T. C. Lubensky, Principles of Condensed Matter Physics, Cambridge University Press (2000).
  (Amazon)
  
  
  
• Particle on a ring and Josephson junction arrays. (Nathan Borggren)
  
  A. Altland, L. I. Glazman, and A. Kamenev, Phys. Rev. Lett., 92, 026801 (2004).
  Electron transport in granular metals., (PDF, subscription required )
  
  
  
• Quantum Spin Hall Effect. (Saul Lapidus)
  
  M. Koenig, H. Buhmann, L. W. Molenkamp, T. L. Hughes, C.-X. Liu, X.-L. Qi, S.-C. Zhang, arXiv:0801.0901v1 [cond-mat.mes-hall] (2008).
  The Quantum Spin Hall Effect: Theory and Experiment, (http://arxiv.org/abs/0801.0901 )
  
  
  
• Topological orders.
  
  X.-G. Wen, Adv. Phys., 44, 405-473 (1995).
  Topological orders and edge excitations in fractional quantum Hall states, (PDF, subscription required )
  
  
  
• Topological order in superconductors with dynamical gauge field.
  
  T. H. Hansson, V. Oganesyan, and S. L. Sondhi, Annals of Physics, 313, 497-538 (2004).
  Superconductors are topologically ordered, (PDF, subscription required )
  
  
  
• Fermionic zero modes in vortex cores.
  
  N. B. Kopnin and M. M. Salomaa, Phys. Rev. B 44, 9667-9677 (1991).
  Mutual friction in superfluid He-3: Effects of bound states in the vortex core, (PDF, subscription required )
  
  
  
• Compact QED in 2+1. Topological defects and mass of photon. (Ozan Erdogan)
  
  A. M. Polyakov, Phys. Lett. B 59, 82-84 (1975).
  Compact gauge fields and infrared catastrophe., (doi:10.1016/0370-2693(75)90162-8 )
  
  A.M. Polyakov, Nucl. Phys. B 120, 429-458 (1977).
  Quark confinement and topology of gauge theories, (doi:10.1016/0550-3213(77)90086-4 )
  
  A.M. Polyakov, Gauge Fields and Strings: Contemporary Concepts in Physics, Volume 3, CRC (1987). (Amazon )
  
  
  
• Compact QED in 2+1 with fermions. Zero modes on topological defects. (Marcos Crighigno)
  
  I. Affleck, J. Harvey, and E. Witten, Nucl. Phys. B 206, 413-439 (1982).
  Instantons and (super-) symmetry breaking in (2+1) dimensions., (doi:10.1016/0550-3213(82)90277-2 )
  
  
  
• Topological defects in spinor BEC condensates with S=1. (Manas Kulkarni)
  
  T.-L. Ho, Phys. Rev. Lett., 81, 742-745 (1998).
  Spinor Bose condensates in optical traps, (doi:10.1103/PhysRevLett.81.742 )
  
  T. Ohmi and K. Machida, J. Phys. Soc. Jpn., 67, 1822-1825 (1998).
  Bose-Einstein condensation with internal degrees of freedom in alkali atom gases, (doi:10.1143/JPSJ.67.1822 )
  
  
  
• Boojums and other exotic defects in He3-A.
  
  
  
• Topologically protected quantum computation.
  
  
  
• Topological versus "spin-wave" transitions in statistical mechanics. XY and Ising models, classical Hesenberg model in three dimensions. (Rafael Lopes de Sa)
  
  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.
  
  O. I. Motrunich, A. Vishwanath, cond-mat/0311222 (2003)
  Emergent Photons and New Transitions in the O(3) Sigma Model with Hedgehog Suppression.
  
  
  
• Geometric phase associated with instantons for two-dimensional quantum Heisenberg model. (Christopher Winterowd)
  
  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.
  
  
  
• Topological order. Boundary states of spin chains (experiment). (Sriram Ganeshan)
  
  M. Hagiwara et. al., Physica B, 177, 386 (1992).
  Magnetization process of an S=1 impure linear chain Heisenberg antiferromagnet.