Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866929389868941312 |
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| author | Lindoy, Lachlan P. Kloss, Benedikt Reichman, David R. |
| author_facet | Lindoy, Lachlan P. Kloss, Benedikt Reichman, David R. |
| contents | The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to $10^6$ bath modes, and find that for these problems the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH, and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to $\sim 1.3\times 10^9$ parameters to obtain accurate dynamics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2109_03134 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator Lindoy, Lachlan P. Kloss, Benedikt Reichman, David R. Chemical Physics The multi-layer multiconfiguration time-dependent Hartree (ML-MCTDH) approach suffers from numerical instabilities whenever the wavefunction is weakly entangled. These instabilities arise from singularities in the equations of motion (EOMs) and necessitate the use of a regularization parameter. The Projector Splitting Integrator (PSI) has previously been presented as an approach for evolving ML-MCTDH wavefunctions that is free of singularities. Here we will discuss the implementation of the multi-layer PSI with a particular focus on how the steps required relate to those required to implement standard ML-MCTDH. We demonstrate the efficiency and stability of the PSI for large ML-MCTDH wavefunctions containing up to hundreds of thousands of nodes by considering a series of spin-boson models with up to $10^6$ bath modes, and find that for these problems the PSI requires roughly 3-4 orders of magnitude fewer Hamiltonian evaluations and 2-3 orders of magnitude fewer Hamiltonian applications than standard ML-MCTDH, and 2-3/1-2 orders of magnitude fewer evaluations/applications than approaches that use improved regularization schemes. Finally, we consider a series of significantly more challenging multi-spin-boson models that require much larger numbers of single-particle functions with wavefunctions containing up to $\sim 1.3\times 10^9$ parameters to obtain accurate dynamics. |
| title | Time Evolution of ML-MCTDH Wavefunctions II: Application of the Projector Splitting Integrator |
| topic | Chemical Physics |
| url | https://arxiv.org/abs/2109.03134 |