Stochastic Adaptive Single-Site Time-Dependent Variational Principle

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.

5 pages, 4 figures

References in corpus (9)

• Real time evolution using the density matrix renormalization group
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Entanglement spectrum in one-dimensional systems
• The Density Matrix Renormalization Group in Chemistry and Molecular Physics: Recent Developments and New Challenges
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Time evolution algorithms for Matrix Product States and DMRG
• Time Dependent Variational Principle with Ancillary Krylov Subspace
• Quantum dynamics simulation of intramolecular singlet fission in covalently linked tetracene dimer
• Dynamically Evolving Bond-Dimensions within the one-site Time-Dependent-Variational-Principle method for Matrix Product States: Towards efficient simulation of non-equilibrium open quantum dynamics

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• Enhanced Krylov Methods for Molecular Hamiltonians: Reduced Memory Cost and Complexity Scaling via Tensor Hypercontraction
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