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

• URL: http://arxiv.org/abs/2307.16031v1
• Date: Sat, 29 Jul 2023 17:41:27 GMT
• Title: Splitting the local Hilbert space: MPS-based approach to large local dimensions
• Authors: Naushad Ahmad Kamar and Mohammad Maghrebi
• Abstract summary: A large, or even infinite, local Hilbert space dimension poses a significant computational challenge for simulating quantum systems. We present a matrix product state (MPS)-based method for simulating one-dimensional quantum systems with a large local Hilbert space dimension.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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.

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