Lieb-Robinson Bound and Adiabatic Evolution
Quantum Physics
2013-07-16 v1
Abstract
We extend the concept of locality to enclose a situation where a tensor-product structure for the Hilbert space is not \textit {a priori} assumed; rather, this locality is related to a given matrix representation of the Hamiltonian associated to the system. As a result, we formulate a Lieb-Robinson-like bound for Hamiltonians local in a given basis. In particular, we employ this bound to obtain alternatively the adiabatic condition, where adiabaticity is naturally ensued from a locality in energy basis and a relatively small Lieb-Robinson bound.
Cite
@article{arxiv.1307.3726,
title = {Lieb-Robinson Bound and Adiabatic Evolution},
author = {M. M. R. Koochakie and S. Alipour and A. T. Rezakhani},
journal= {arXiv preprint arXiv:1307.3726},
year = {2013}
}