Importance of Appropriately Regularizing the ML-MCTDH Equations of Motion
| Autor: | Hans-Dieter Meyer, Haobin Wang |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
010304 chemical physics
Generalization Chemistry Hilbert space Equations of motion Hartree Function (mathematics) 010402 general chemistry 01 natural sciences Regularization (mathematics) 0104 chemical sciences symbols.namesake Singularity 0103 physical sciences symbols Applied mathematics Physics::Atomic Physics Tensor Physics::Chemical Physics Physical and Theoretical Chemistry |
| Zdroj: | The journal of physical chemistry. A. 125(15) |
| ISSN: | 1520-5215 |
| Popis: | The multiconfiguration time-dependent Hartree (MCTDH) method and its generalization, the multilayer MCTDH (ML-MCTDH), result in equations of motion (EOMs) that are singular when there are virtual orbitals-the unoccupied single-particle functions-in the wave function expansion. For decades this singularity had been numerically removed by regularizing the reduced density matrix. In this Perspective we discuss our recent proposal to regularize the coefficient tensor instead, which has significant impact on both the efficiency and correctness of the EOMs in MCTDH and ML-MCTDH for challenging problems. We further demonstrate that when the system becomes large such that it is necessary to use ML-MCTDH with many layers, it is much more important to employ this new regularization scheme. We illustrate this point by studying a spin-boson model with a large bath that contains up to 100 000 modes. We show that even in the weak coupling regime the new regularization scheme is required to quickly rotate the virtual orbitals into the correct directions in Hilbert space. We argue that this situation can be common for applying a time-dependent tensor network approach to any large enough system. |
| Databáze: | OpenAIRE |
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