Finite Group Velocity Implies Locality of Interactions
METADATA ONLY
Loading...
Author / Producer
Date
2020-06-17
Publication Type
Working Paper
ETH Bibliography
yes
Citations
Altmetric
METADATA ONLY
Data
Rights / License
Abstract
Spin systems with exponentially decaying k-body interactions have an effective finite group velocity for the propagation of correlations due to Lieb-Robinson bounds. We show that a finite group velocity conversely implies the locality of the underlying Hamiltonian: a system fulfills Lieb-Robinson bounds in exponential form if and only if the underlying interactions decay exponentially in space. Our result already follows from the behaviour of two-point correlation functions for single-site observables and generalizes to different decay behaviours. As a side-result, we thus find that Lieb-Robinson bounds for single-site observables imply Lieb-Robinson bounds for arbitrary bounded observables. In addition we show that our results generalize to fermionic lattice models.
Permanent link
Publication status
published
External links
Editor
Book title
Journal / series
Volume
Pages / Article No.
Publisher
Cornell University
Event
Edition / version
Methods
Software
Geographic location
Date collected
Date created
Subject
Organisational unit
03781 - Renner, Renato / Renner, Renato
Notes
Funding
Related publications and datasets
Is previous version of: