Lieb-Robinson bounds with dependence on interaction strengths
Abstract
We propose new Lieb-Robinson bounds (bounds on the speed of propagation of information in quantum systems) with an explicit dependence on the interaction strengths of the Hamiltonian. For systems with more than two interactions it is found that the Lieb-Robinson speed is not always algebraic in the interaction strengths. We consider Hamiltonians with any finite number of bounded operators and also a certain class of unbounded operators. We obtain bounds and propagation speeds for quantum systems on lattices and also general graphs possessing a kind of homogeneity and isotropy. One area for which this formalism could be useful is the study of quantum phase transitions which occur when interactions strengths are varied.
Keywords
Cite
@article{arxiv.1002.4190,
title = {Lieb-Robinson bounds with dependence on interaction strengths},
author = {Isabeau Prémont-Schwarz and Jeff Hnybida},
journal= {arXiv preprint arXiv:1002.4190},
year = {2014}
}
Comments
19 pages, 1 figure, minor modifications