  By using the properties of orthogonal polynomials, we present an exact
unitary transformation that maps the Hamiltonian of a quantum system coupled
linearly to a continuum of bosonic or fermionic modes to a Hamiltonian that
describes a one-dimensional chain with only nearest-neighbour interactions.
This analytical transformation predicts a simple set of relations between the
parameters of the chain and the recurrence coefficients of the orthogonal
polynomials used in the transformation, and allows the chain parameters to be
computed using numerically stable algorithms that have been developed to
compute recurrence coefficients. We then prove some general properties of this
chain system for a wide range of spectral functions, and give examples drawn
from physical systems where exact analytic expressions for the chain properties
can be obtained. Crucially, the short range interactions of the effective chain
system permits these open quantum systems to be efficiently simulated by the
density matrix renormalization group methods.
