New Anomalous Lieb-Robinson Bounds in Quasiperiodic XY Chains

作者：Damanik David^*; Lemm Marius; Lukic Milivoje; Yessen William

来源：Physical Review Letters, 2014, 113(12): 127202.

DOI：10.1103/PhysRevLett.113.127202

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 vertical bar x vertical bar %26lt;= nu vertical bar t vertical bar, we obtain vertical bar x vertical bar %26lt;= nu vertical bar t vertical bar(alpha) for some 0 %26lt; alpha %26lt; 1. We can characterize the allowed values of a exactly as those exceeding the upper transport exponent alpha(+)(u) of a one-body Schrodinger 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.

• 出版日期2014-9-18