Lieb-Robinson bounds imply locality of interactions
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Lieb-Robinson bounds imply locality of interactions. / Wilming, Henrik; Werner, Albert H.
I: Physical Review B, Bind 105, Nr. 12, 125101, 02.03.2022.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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TY - JOUR
T1 - Lieb-Robinson bounds imply locality of interactions
AU - Wilming, Henrik
AU - Werner, Albert H.
PY - 2022/3/2
Y1 - 2022/3/2
N2 - Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed-matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviors as well as fermionic lattice models. As a side result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.
AB - Discrete lattice models are a cornerstone of quantum many-body physics. They arise as effective descriptions of condensed-matter systems and lattice-regularized quantum field theories. Lieb-Robinson bounds imply that if the degrees of freedom at each lattice site only interact locally with each other, correlations can only propagate with a finite group velocity through the lattice, similarly to a light cone in relativistic systems. Here we show that Lieb-Robinson bounds are equivalent to the locality of the interactions: a system with k-body interactions fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. In particular, our result already follows from the behavior of two-point correlation functions for single-site observables and generalizes to different decay behaviors as well as fermionic lattice models. As a side result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for bounded observables with arbitrary support.
KW - SPECTRAL GAP
KW - QUANTUM
KW - PROPAGATION
KW - EXISTENCE
KW - SYSTEMS
U2 - 10.1103/PhysRevB.105.125101
DO - 10.1103/PhysRevB.105.125101
M3 - Journal article
VL - 105
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 12
M1 - 125101
ER -
ID: 302386655