Splitting the local Hilbert space: MPS-based approach to large local dimensions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866913470226628608 |
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| author | Kamar, Naushad Ahmad Maghrebi, Mohammad |
| author_facet | Kamar, Naushad Ahmad Maghrebi, Mohammad |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_16031 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Splitting the local Hilbert space: MPS-based approach to large local dimensions Kamar, Naushad Ahmad Maghrebi, Mohammad Quantum Physics Quantum Gases Strongly Correlated Electrons 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. |
| title | Splitting the local Hilbert space: MPS-based approach to large local dimensions |
| topic | Quantum Physics Quantum Gases Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2307.16031 |