title: New anomalous Lieb-Robinson bounds in quasiperiodic XY chains.
abstract: We announce and sketch the rigorous proof of a new kind of anomalous (or sub-ballistic) Lieb-Robinson (LR) bound for an isotropic XY chain in a quasiperiodic transversal magnetic field. Instead of the usual effective light cone |x|≤v|t|, we obtain |x|≤v|t|α for some 0<α<1. We can characterize the allowed values of α exactly as those exceeding the upper transport exponent αu+ of a one-body Schrödinger operator. To our knowledge, this is the first rigorous derivation of anomalous quantum many-body transport. We also discuss anomalous LR bounds with power-law tails for a random dimer field.
authors.affiliation: Department of Mathematics, Rice University, Houston, Texas 77005, USA.
authors.forename: David
authors.initials: D
authors.lastname: Damanik
authors.affiliation: Department of Mathematics, California Institute of Technology, Pasadena, California 91125, USA.
authors.forename: Marius
authors.initials: M
authors.lastname: Lemm
authors.affiliation: Department of Mathematics, Rice University, Houston, Texas 77005, USA.
authors.forename: Milivoje
authors.initials: M
authors.lastname: Lukic
authors.affiliation: Department of Mathematics, Rice University, Houston, Texas 77005, USA.
authors.forename: William
authors.initials: W
authors.lastname: Yessen