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

TL;DR

This paper introduces an MPS-based method that splits large local Hilbert spaces into smaller parts, enabling efficient simulation of one-dimensional quantum systems with large local dimensions, demonstrated on the spin-boson model.

Contribution

The authors develop a novel Hilbert space splitting technique integrated into MPS methods, allowing simulation of systems with large local dimensions without altering existing algorithms.

Findings

Method achieves accurate simulation of the spin-boson model.

Excellent agreement with previous studies validates the approach.

Eases simulation of bosonic systems with large on-site populations.

Abstract

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.