Details
| Original language | English |
|---|---|
| Article number | 125101 |
| Journal | Physical Review B |
| Volume | 105 |
| Issue number | 12 |
| Publication status | Published - 15 Mar 2022 |
| Externally published | Yes |
Abstract
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.
ASJC Scopus subject areas
- Materials Science(all)
- Electronic, Optical and Magnetic Materials
- Physics and Astronomy(all)
- Condensed Matter Physics
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In: Physical Review B, Vol. 105, No. 12, 125101, 15.03.2022.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Lieb-Robinson bounds imply locality of interactions
AU - Wilming, Henrik
AU - Werner, Albert H.
N1 - Funding Information: We would like to thank Terry Farrelly and Zoltán Zimborás for interesting comments and discussions. H.W. acknowledges support through the National Centre of Competence in Research, Quantum Science and Technology (QSIT). A.H.W. thanks the VILLUM FONDEN for its support with a Villum Young Investigator Grant (Grant No. 25452) and its support via the QMATH Centre of Excellence (Grant No. 10059).
PY - 2022/3/15
Y1 - 2022/3/15
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.
UR - http://www.scopus.com/inward/record.url?scp=85126437608&partnerID=8YFLogxK
U2 - 10.1103/PhysRevB.105.125101
DO - 10.1103/PhysRevB.105.125101
M3 - Article
AN - SCOPUS:85126437608
VL - 105
JO - Physical Review B
JF - Physical Review B
SN - 2469-9950
IS - 12
M1 - 125101
ER -