Constructing tensor network influence functionals for general quantum dynamics

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.