title: Simulating Bosonic Baths with Error Bars.
abstract: We derive rigorous truncation-error bounds for the spin-boson model and its generalizations to arbitrary quantum systems interacting with bosonic baths. For the numerical simulation of such baths, the truncation of both the number of modes and the local Hilbert-space dimensions is necessary. We derive superexponential Lieb-Robinson-type bounds on the error when restricting the bath to finitely many modes and show how the error introduced by truncating the local Hilbert spaces may be efficiently monitored numerically. In this way we give error bounds for approximating the infinite system by a finite-dimensional one. As a consequence, numerical simulations such as the time-evolving density with orthogonal polynomials algorithm (TEDOPA) now allow for the fully certified treatment of the system-environment interaction.
authors.affiliation: Institut für Theoretische Physik, Universität Ulm, Ulm D-89069, Germany.|Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: M P
authors.initials: MP
authors.lastname: Woods
authors.affiliation: Institut für Theoretische Physik, Universität Ulm, Ulm D-89069, Germany.
authors.forename: M
authors.initials: M
authors.lastname: Cramer
authors.affiliation: Institut für Theoretische Physik, Universität Ulm, Ulm D-89069, Germany.|Quantum Optics and Laser Science, Blackett Laboratory, Imperial College London, London SW7 2AZ, United Kingdom.
authors.forename: M B
authors.initials: MB
authors.lastname: Plenio