Lieb–Robinson bound in one-dimensional inhomogeneous quantum systems

Abstract

Lieb–Robinson bound (LRB) in one-dimensional noninteracting many-electron systems with the disordered and quasiperiodic on-site potentials is studied numerically. For the short-range hopping system, a logarithmic light cone (i.e. |x|=βlogt+x0) is found in the system with the disordered on-site potential for small time. The coefficient β decreases with the increasing strength of disordered. When time is large, the bound does not change with time (i.e. |x|=C). For the generalized Fibonacci quasiperiodic (GFQ) system, the on-site potential is taken as V or −V according to two kinds of GFQ sequences. It is found that the system has a power-law light cone (i.e. |x|∝tγ, with 0<γ<1). The exponent γ decreases with the increasing V. We also find that γ for the first class of GFQ system is larger than that for the second class of GFQ system with the same V. Finally, the effects of the long-range hopping which decays like r−α with the distance r on LRB are discussed.