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Quantum lattice models with large local Hilbert spaces emerge across variousfields in quantum many-body physics. Problems such as the interplay betweenfermions and phonons, the BCS-BEC crossover of interacting bosons, ordecoherence in quantum simulators have been extensively studied boththeoretically and experimentally. In recent years, tensor network methods havebecome 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 $U(1)$ symmetriesfor any type of lattice model. Exploiting the generated symmetries, numericalexpenses that are related to the local degrees of freedom decreasesignificantly. This allows for an efficient treatment of systems with largelocal dimensions. Further exploring this mapping, we reveal an intimateconnection between the Schmidt values of the corresponding matrix-product-staterepresentation and the single-site reduced density matrix. Our findingsmotivate an intuitive physical picture of the truncations occurring in typicalalgorithms and we give bounds on the numerical complexity in comparison tostandard methods that do not exploit such artificial symmetries. We demonstratethis new mapping, provide an implementation recipe for an existing code, andperform example calculations for the Holstein model at half filling. We studiedsystems with a very large number of lattice sites up to $L=501$ whileaccounting for $N_{\rm ph}=63$ phonons per site with high precision in the CDWphase.

Efficient and Flexible Approach to Simulate Low-Dimensional Quantum Lattice Models with Large Local Hilbert Spaces