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arXiv · 2110.12703

Stochastic Adaptive Single-Site Time-Dependent Variational Principle

Yihe Xu·Zhaoxuan Xie·Xiaoyu Xie·Ulrich Schollwöck·Haibo Ma
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Abstract

In recent years, the time-dependent variational principle (TDVP) method based on the matrix product state (MPS) wave function formulation has shown its great power in performing large-scale quantum dynamics simulations for realistic chemical systems with strong electron-vibration interactions. In this work, we propose a new stochastic adaptive single-site TDVP (SA-1TDVP) scheme to evolve the bond-dimension adaptively, which can integrate the tra-ditional advantages of both the high efficiency of single-site TDVP (1TDVP) variant and the high accuracy of the two-site TDVP (2TDVP) variant. Based on the assumption that the level statistics of entanglement Hamiltonians, which originate from the reduced density matrices of the MPS method, follows a Poisson or Wigner distribution, as generically predicted by random matrix theory, addi-tional random singular values are generated to expand the bond-dimension automatically. Tests on simulating the vibrationally-resolved quantum dynamics and absorption spectra in the pyrazine molecule and perylene bisimide (PBI) J-aggregate trimer as well as a spin-1/2 Heisenberg chain show that it can be automatic and as accurate as 2TDVP but reduce the computational time remarkably.

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Yihe Xu, Zhaoxuan Xie, Xiaoyu Xie, Ulrich Schollwöck, Haibo Ma. 2021-10-25. Stochastic Adaptive Single-Site Time-Dependent Variational Principle. https://doi.org/10.1021/jacsau.1c00474

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