PIRSA:13040125 Scientific Series Condensed Matter

DOI10.48660/13040125

Series: Quantum Matter

Moore, J. (2013). Quantum transport in one dimension: from integrability to many-body localization and topology. Perimeter Institute. https://pirsa.org/13040125

Moore, Joel. Quantum transport in one dimension: from integrability to many-body localization and topology. Perimeter Institute, Apr. 23, 2013, https://pirsa.org/13040125 

@misc{ pirsa_PIRSA:13040125,
  doi = {10.48660/13040125},
  url = {https://pirsa.org/13040125},
  author = {Moore, Joel},
  keywords = {Condensed Matter},
  language = {en},
  title = {Quantum transport in one dimension: from integrability to many-body localization and topology},
  publisher = {Perimeter Institute},
  year = {2013},
  month = {apr},
  note = {PIRSA:13040125 see, \url{https://pirsa.org}}
}

Abstract

Recent advances in analytical theory and numerical methods enable some long-standing questions about transport in one dimension to be answered; these questions are closely related to transport experiments in quasi-1D compounds.  The spinless fermion chain with nearest-neighbor interactions at half-filling, or equivalently the XXZ model in zero magnetic field, is an example of an integrable system in which no conventional conserved quantity forces dissipationless transport (Drude weight); we show that there is nevertheless a Drude weight and that at some points its contribution is from a new type of conserved quantity recently constructed by Prosen.  Adding an integrability-breaking perturbation leads to a scaling theory of conductivity at low temperature.  Adding disorder, we study the question of how Anderson localization is modified by interactions when the system remains fully quantum coherent ("many-body localization").  We find that even weak interactions are a singular perturbation on some quantities: entanglement grows slowly but without limit, suggesting that dynamics in the possible many-body localized phase are glass-like.  If time permits, some results on the fractional Luttinger's theorem and the 1D limit of quantum Hall states will be presented.

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