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

Harvard

Wilming, H & Werner, AH 2022, 'Lieb-Robinson bounds imply locality of interactions', Physical Review B, bind 105, nr. 12, 125101. https://doi.org/10.1103/PhysRevB.105.125101

APA

Wilming, H., & Werner, A. H. (2022). Lieb-Robinson bounds imply locality of interactions. Physical Review B, 105(12), [125101]. https://doi.org/10.1103/PhysRevB.105.125101

Vancouver

Wilming H, Werner AH. Lieb-Robinson bounds imply locality of interactions. Physical Review B. 2022 mar. 2;105(12). 125101. https://doi.org/10.1103/PhysRevB.105.125101

Author

Wilming, Henrik ; Werner, Albert H. / Lieb-Robinson bounds imply locality of interactions. I: Physical Review B. 2022 ; Bind 105, Nr. 12.

Bibtex

@article{c224594eea05459a9aef95fa700150ec,
title = "Lieb-Robinson bounds imply locality of interactions",
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.",
keywords = "SPECTRAL GAP, QUANTUM, PROPAGATION, EXISTENCE, SYSTEMS",
author = "Henrik Wilming and Werner, {Albert H.}",
year = "2022",
month = mar,
day = "2",
doi = "10.1103/PhysRevB.105.125101",
language = "English",
volume = "105",
journal = "Physical Review B",
issn = "2469-9950",
publisher = "American Physical Society",
number = "12",

}

RIS

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