Lieb-Robinson Bound at Finite Temperature

Abstract

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.

12 pages, 6 figures

References in corpus (4)

• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• Propagation of Correlations in Quantum Lattice Systems
• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• An upper bound on transport

Cited by in corpus (6)

• Euclidean operator growth and quantum chaos
• Time evolution of correlation functions in quantum many-body systems
• Classifying transport behavior via current fluctuations in open quantum systems
• Time-Polynomial Lieb-Robinson bounds for finite-range spin-network models
• Revealing quantum operator scrambling via measuring Holevo information on digital quantum simulators
• Rate of cluster decomposition via Fermat-Steiner point