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A large, or even infinite, local Hilbert space dimension poses a significantcomputational challenge for simulating quantum systems. In this work, wepresent a matrix product state (MPS)-based method for simulatingone-dimensional quantum systems with a large local Hilbert space dimension, anexample being bosonic systems with a large on-site population. To this end, we\textit{split} the local Hilbert space corresponding to one site into twosites, each with a smaller Hilbert space dimension. An advantage of this methodis that it can be easily integrated into MPS-based techniques such astime-dependent variational principle (TDVP) without changing their standardalgorithmic structure. Here, we implement our method using the TDVP to simulatethe dynamics of the spin-boson model, a prototypical model of a spininteracting with a large bath of bosonic modes. We benchmark our method againstand find excellent agreement with previous studies.

Splitting the local Hilbert space: MPS-based approach to large local dimensions