Lieb-Robinson bound and information propagation in long-range interacting systems

Andrew Y. Guo, Minh C. Tran, Andrew M. Childs +2 more

Takuro Matsuta, Tohru Koma, Shu Nakamura

Zhiqiang Huang, Xiao-Kan Guo

The Lieb-Robinson bound shows that the speed of propagating information in a nonrelativistic quantum lattice system is bounded by a finite velocity, which entails the clustering of correlations. In this paper, we extend the Lieb-Robinson bound to quantum systems at finite temperature by calculating the dynamical correlation function at nonzero temperature for systems whose interactions are, respectively, short range, exponentially decaying, and long range. We introduce a simple way of counting the clusters in a cluster expansion by using the combinatoric generating functions of graphs. Limitations and possible applications of the obtained bound are also discussed.

Zhexuan Gong, Michael Foss‐Feig, Spyridon Michalakis +1 more

Marius Lemm, Carla Rubiliani, Israel Michael Sigal +1 more

The authors study the information transportation capabilities of bosonic quantum many-body systems with long-range interactions. They rigorously prove that initially localized quantum states exhibit a linear Lieb-Robinson light cone for information propagation and they derive consequences of this result, e.g., bounds on quantum messaging and quantum state control.

Miles D. Miller-Dickson, Christopher Rose