New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains
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 α+u 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.
Damanik, David, Lemm, Marius, Lukic, Milivoje, et al.. "New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains." Physical Review Letters, 113, no. 12 (2014) American Physical Society: 127202. http://dx.doi.org/10.1103/PhysRevLett.113.127202.