Dynamical error bounds for continuum discretization via Gauss quadrature rules – a Lieb-Robinson bound approach

Dynamical error bounds for continuum discretization via Gauss quadrature rules – a Lieb-Robinson bound approachThe interaction of a quantum system with its environment is of fundamental importance for the development of quantum technologies. The spin-boson model in which a spin degree of freedom couples to a continuum of harmonic oscillators is one of the most fundamental models in this area. A continuum of harmonic oscillators is not easy to treat numerically and ideally one would like to reduce them to a finite number of harmonic oscillators, i.e. to discretize the harmonic environment. This will make us to commit errors that we need to bound. Our work uses a chain mapping that we had developed earlier together with Lieb-Robinson type methods which limit the speed at which perturbation travel through such chains to develop such error bounds.