Propagation of Correlations in Quantum Lattice Systems

By Bruno Nachtergaele, Y. Ogata, Robert Sims. 2006

252 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/9fe1d798b37b1c548bc7b6e8d5180c20b6e0daea

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In Atomic and Molecular Physics, and Optics

In Statistics and Probability

Citations in the corpus

A Rigorous Theory of Many-Body Prethermalization for Periodically Driven and Closed Quantum Systems (2015, background): “17 following it) in [31], with obvious adaptations to the notation and setup of the present paper (for example; the function F is chosen as F (r) = e(1 + r)).”
Stability of Frustration-Free Hamiltonians (2011, methodology): “We make extensive use of Lieb-Robinson bounds [28], both for the evolution of operators according to the Hamiltonians under consideration [15,19,30–34,39,40], as well as Lieb-Robinson bounds on the quasi-adiabatic evolution, or spectral flow, of gapped eigenspaces [3,17,20].”
Light-cone-like spreading of correlations in a quantum many-body system (2011, background): “0(5) Er (the number in parenthesis denotes the uncertainty of the last digit; see Methods), where Er~ 2pB ð Þ(2)= 8ma(2)lat is the recoil energy of the lattice and m the atomic mass of (87)Rb.”
Automorphic Equivalence within Gapped Phases of Quantum Lattice Systems (2011, unknown): “If dimH2 <∞, one can simply take A′ = 1 dimH2 TrH2A, as is done in [9, 36] (or see (i) in the proof of Lemma 3.”
Non-local propagation of correlations in quantum systems with long-range interactions (2014, unknown): “As a result of (1), the connected correlation at t 5 0 vanishes (ÆAiAjæc 5 0).”
Locality of temperature (2013, methodology): “[29] B.”