This page is a summary of the discussions during the Fractionalization Phenomena session.

Talk: X. L. Qi
  • How many mass terms can you generate on edge of QSH system from a 3 component magnetic field? Without disorder it seems like you only get two possible mass terms. With disorder the answer is unknown currently, but in that case you can probably get 3 .
  • It is difficult to measure exactly half charge (e/2) much easier to measure a charge difference of e/2.
  • Can you insert generic spin flux without closing the bulk energy gap? In general no, but maybe the set of points where the gap closes has measure zero.
  • Does the QSH edge have fractional excitations? Yes and no, if you externally impose a magnetic domain wall then no. If interactions are string enough to spontaneously break time-reversal symmetry then it is possible to have e/2 charged "domain-wall" excitations.
  • Compare spin-charge separation, with Kane and Fu work on Z_2 pumping.
  • What is quantized in quantum spin Hall?

Talk: C. Kallin
  • What is the dynamics of the relative phase? It is gapped by a Higgs mechanism.
  • Relation between S_z conservation and instantons.
  • There are 2 U(1) phases in each layer.
  • Mass generation for 1d fermions on edge given by coupling to a U(1) field.
  • Is there any coupling between spinons and a physical electro-magnetic field? Possibly a small coupling due to a finite system size?
  • The topological mott insulator paper, and this model start from interactions with no spin-orbit coupling and dynamically generate it. What about starting from interactions + spin orbit coupling and looking for phases of matter?
Talk: Y. Hatsugai
Talk: Y. Oreg
  • Can you think about it as similar to QSH? Not exactly because fractional charge will depend on electron-electron interactions.
Talk: A. Vishwanath
  • What happens in the case \nu_0=1 but \nu_1\nu_2\nu_3= (000)? This is a strong topological insulator with dirac node near \Gamma point in k-space.
  • Can disorder and perturbations destroy the dislocations? Can shrink to zero size, but they will act like vortices.
  • Can you imagine a case where these defects proliferate?
  • Loops that are closed and isolated do not have exact zero modes.
  • Can you get more than one set of modes?
  • For quantum Hall they have to always have a partner defect, cannot exist alone (Fermion doubling problem).