## Lieb-Robinson Bound and Adiabatic Evolution    [PDF]

M. M. R. Koochakie, S. Alipour, A. T. Rezakhani
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.
View original: http://arxiv.org/abs/1307.3726