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This study introduces an iterative method to calculate quantum dynamics, using tensor networks to efficiently approximate influence functionals. This approach enables accurate quantum simulations for extended periods, overcoming limitations of direct time evolution.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Computational physics

Background:

  • Accurately simulating quantum dynamics of open systems is computationally challenging.
  • Existing methods often rely on approximations like linear coupling to quadratic baths.
  • Developing efficient numerical techniques is crucial for understanding complex quantum phenomena.

Purpose of the Study:

  • To develop an iterative formalism for computing influence functionals beyond standard approximations.
  • To investigate the approximability of influence functionals using space-time tensor networks.
  • To enable accurate and efficient quantum dynamics simulations for subsystems interacting with baths.

Main Methods:

  • Developed an iterative formalism for influence functional computation.
  • Employed space-time tensor network representations.
  • Analyzed approximability via bond dimension and time-like entanglement.
  • Studied the spin-boson model and interacting hard-core bosons in a 1D trap.

Main Results:

  • Influence functionals and their intermediates can be efficiently approximated by low bond dimension tensor networks in specific regimes.
  • This tensor network approach allows for accurate quantum dynamics computation over longer timescales compared to direct methods.
  • The construction of the influence functional involves non-trivial cancellations due to evolving correlations.

Conclusions:

  • The proposed iterative formalism and tensor network representation offer an efficient pathway for simulating quantum dynamics.
  • The method demonstrates potential for overcoming limitations of traditional simulation techniques.
  • Efficient approximation of influence functionals is achievable, paving the way for advanced quantum system studies.