Stochastic Adaptive Single-Site Time-Dependent Variational Principle

TL;DR

This paper introduces a stochastic adaptive single-site TDVP method that automatically adjusts bond-dimension, combining efficiency and accuracy for large-scale quantum dynamics simulations, demonstrated on molecular and spin chain systems.

Contribution

It proposes a novel stochastic adaptive single-site TDVP scheme that adaptively expands bond-dimension based on entanglement level statistics, improving efficiency without sacrificing accuracy.

Findings

Achieves accuracy comparable to two-site TDVP.

Reduces computational time significantly.

Successfully applied to molecular vibrational dynamics and spin chains.

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.