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Stochastic Adaptive Single-Site Time-Dependent Variational Principle.

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We developed a stochastic adaptive single-site TDVP (SA-1TDVP) method for quantum dynamics. This approach enhances accuracy and efficiency in simulating complex chemical systems with strong electron-vibration interactions.

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Area of Science:

  • Quantum dynamics simulations
  • Computational chemistry
  • Condensed matter physics

Background:

  • Matrix product state (MPS) formulation of the time-dependent variational principle (TDVP) is powerful for quantum dynamics.
  • Strong electron-vibration interactions in realistic chemical systems pose simulation challenges.

Purpose of the Study:

  • To introduce a novel stochastic adaptive single-site TDVP (SA-1TDVP) scheme.
  • To improve the adaptive evolution of bond-dimension in MPS-based TDVP.
  • To combine the efficiency of single-site TDVP (1TDVP) with the accuracy of two-site TDVP (2TDVP).

Main Methods:

  • Developed a SA-1TDVP scheme for adaptive bond-dimension evolution.
  • Utilized random-matrix theory predictions for entanglement Hamiltonian level statistics (Poisson or Wigner distributions).
  • Generated random singular values to automatically expand bond-dimension.

Main Results:

  • SA-1TDVP demonstrated automatic and accurate bond-dimension evolution.
  • Achieved accuracy comparable to the two-site TDVP (2TDVP) method.
  • Significantly reduced computational time compared to traditional methods.

Conclusions:

  • The SA-1TDVP method offers a computationally efficient and accurate approach for quantum dynamics.
  • This method is effective for simulating vibrationally resolved quantum dynamics and spectra.
  • Applicable to diverse systems including molecules and spin chains.