Stochastic Adaptive Single-Site Time-Dependent Variational Principle

Xu, Yihe; Xie, Zhaoxuan; Xie, Xiaoyu; Schollwoeck, Ulrich und Ma, Haibo (2022): Stochastic Adaptive Single-Site Time-Dependent Variational Principle. In: JACS Au, Vol. 2, No. 2: pp. 335-340

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 stochastic adaptive single-site TDVP (SA-1TDVP) scheme to evolve the bond-dimension adaptively, which can integrate the traditional advantages of both the high efficiency of the 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, additional 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.

• Item Type: Journal article
• Faculties: Physics
• Subjects: 500 Science > 530 Physics
• Language: English
• DFG: Gefördert durch die Deutsche Forschungsgemeinschaft (DFG) - 390814868