Signaling and scrambling with strongly long-range interactions
Andrew Y. Guo, Minh C. Tran, Andrew M. Childs, Alexey V. Gorshkov, Zhexuan Gong
Abstract
Strongly long-range interacting quantum systems---those with interactions decaying as a power law $1/{r}^{\ensuremath{\alpha}}$ in the distance $r$ on a $D$-dimensional lattice for $\ensuremath{\alpha}\ensuremath{\le}D$---have received significant interest in recent years. They are present in leading experimental platforms for quantum computation and simulation, as well as in theoretical models of quantum-information scrambling and fast entanglement creation. Since no notion of locality is expected in such systems, a general understanding of their dynamics is lacking. In a step towards rectifying this problem, we prove two Lieb-Robinson-type bounds that constrain the time for signaling and scrambling in strongly long-range interacting systems, for which no tight bounds were previously known. Our first bound applies to systems mappable to free-particle Hamiltonians with long-range hopping, and is saturable for $\ensuremath{\alpha}\ensuremath{\le}D/2$. Our second bound pertains to generic long-range interacting spin Hamiltonians and gives a tight lower bound for the signaling time to extensive subsets of the system for all $\ensuremath{\alpha}<D$. This many-site signaling time lower bounds the scrambling time in strongly long-range interacting systems.