Moore, J. (2013). Quantum transport in one dimension: from integrability to many-body localization and topology. Perimeter Institute for Theoretical Physics. https://pirsa.org/13040125
MLA
Moore, Joel. Quantum transport in one dimension: from integrability to many-body localization and topology. Perimeter Institute for Theoretical Physics, Apr. 23, 2013, https://pirsa.org/13040125
BibTex
@misc{ scivideos_PIRSA:13040125,
doi = {10.48660/13040125},
url = {https://pirsa.org/13040125},
author = {Moore, Joel},
keywords = {Quantum Matter},
language = {en},
title = {Quantum transport in one dimension: from integrability to many-body localization and topology},
publisher = {Perimeter Institute for Theoretical Physics},
year = {2013},
month = {apr},
note = {PIRSA:13040125 see, \url{https://scivideos.org/pirsa/13040125}}
}
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.