Lieb-Robinson Bounds and the Exponential Clustering Theorem

Abstract

We give a Lieb-Robinson bound for the group velocity of a large class of discrete quantum systems which can be used to prove that a non-vanishing spectral gap implies exponential clustering in the ground state of such systems.

v2: corrected proof of Theorem 2. v3: slightly better bound in Theorem 2; updated proof

References in corpus (6)

• Statistical mechanics of complex networks
• Lieb-Schultz-Mattis in Higher Dimensions
• Locality in Quantum and Markov Dynamics on Lattices and Networks
• The spectral gap for some spin chains with discrete symmetry breaking
• Mean-Field and Anomalous Behavior on a Small-World Network
• Classical XY Model in 1.99 Dimensions

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