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

A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. In this work, we present a matrix product state (MPS)-based method for simulating one-dimensional quantum systems with a large local Hilbert space dimension, an example being bosonic systems with a large on-site population. To this end, we \textit{split} the local Hilbert space corresponding to one site into two sites, each with a smaller Hilbert space dimension. An advantage of this method is that it can be easily integrated into MPS-based techniques such as time-dependent variational principle (TDVP) without changing their standard algorithmic structure. Here, we implement our method using the TDVP to simulate the dynamics of the spin-boson model, a prototypical model of a spin interacting with a large bath of bosonic modes. We benchmark our method against and find excellent agreement with previous studies.