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.
Original language | English |
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Article number | 125101 |
Journal | Physical Review B |
Volume | 105 |
Issue number | 12 |
Number of pages | 11 |
ISSN | 2469-9950 |
DOIs | |
Publication status | Published - 2 Mar 2022 |
Keywords
- SPECTRAL GAP
- QUANTUM
- PROPAGATION
- EXISTENCE
- SYSTEMS