Propagation of Correlations in Quantum Lattice Systems

Abstract

We provide a simple proof of the Lieb-Robinson bound and use it to prove the existence of the dynamics for interactions with polynomial decay. We then use our results to demonstrate that there is an upper bound on the rate at which correlations between observables with separated support can accumulate as a consequence of the dynamics.

10 pages

References in corpus (3)

• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
• General entanglement scaling laws from time evolution

Cited by in corpus (8)

• Autocorrelations and Thermal Fragility of Anyonic Loops in Topologically Quantum Ordered Systems
• Lieb-Robinson Bounds for Harmonic and Anharmonic Lattice Systems
• A Multi-Dimensional Lieb-Schultz-Mattis Theorem
• Lieb-Robinson bounds and the speed of light from topological order
• Quantum Dynamics with Mean Field Interactions: a New Approach
• Approximating the ground state of gapped quantum spin systems
• Entanglement in Finitely Correlated Spin States
• On Spectral Gap,U(1) Symmetry and Split Property in Quantum Spin Chains