  Quantum lattice models with large local Hilbert spaces emerge across various
fields in quantum many-body physics. Problems such as the interplay between
fermions and phonons, the BCS-BEC crossover of interacting bosons, or
decoherence in quantum simulators have been extensively studied both
theoretically and experimentally. In recent years, tensor network methods have
become one of the most successful tools to treat lattice systems numerically.
Nevertheless, systems with large local Hilbert spaces remain challenging. Here,
we introduce a mapping that allows to construct artificial $U(1)$ symmetries
for any type of lattice model. Exploiting the generated symmetries, numerical
expenses that are related to the local degrees of freedom decrease
significantly. This allows for an efficient treatment of systems with large
local dimensions. Further exploring this mapping, we reveal an intimate
connection between the Schmidt values of the corresponding matrix-product-state
representation and the single-site reduced density matrix. Our findings
motivate an intuitive physical picture of the truncations occurring in typical
algorithms and we give bounds on the numerical complexity in comparison to
standard methods that do not exploit such artificial symmetries. We demonstrate
this new mapping, provide an implementation recipe for an existing code, and
perform example calculations for the Holstein model at half filling. We studied
systems with a very large number of lattice sites up to $L=501$ while
accounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDW
phase.
