Tree tensor network hierarchical equations of motion based on time-dependent variational principle for efficient open...

Area of Science:

• Quantum Dynamics
• Computational Physics
• Quantum Information Science

Background:

• Simulating open quantum systems interacting with structured environments is computationally challenging.
• Existing methods like Hierarchical Equations of Motion (HEOM) struggle with complex system-bath interactions.
• Accurate modeling is crucial for understanding phenomena like dephasing and relaxation in quantum systems.

Purpose of the Study:

• To introduce an efficient and exact method for calculating open quantum dynamics.
• To enable the simulation of driven quantum systems interacting with highly structured bosonic baths.
• To provide a general-purpose computational tool for these simulations.

Main Methods:

• Combining tree tensor network (TTN) decomposition with a generalized hierarchical equations of motion (HEOM).
• Developing a series of quantum master equations for TTN core tensors using the time-dependent Dirac-Frenkel variational principle.
• Implementing the TENSO Python code with fixed-rank and adaptive-rank propagators for TTN-HEOM dynamics.

Main Results:

• The TTN-HEOM method accurately captures non-Markovian dynamics to all orders in system-bath interaction.
• The computational cost is affordable, enabling simulations beyond the capabilities of standard HEOM.
• Demonstrated simulation of a two-level system coupled to a complex structured bath.

Conclusions:

• TTN-HEOM offers an efficient and accurate approach for simulating open quantum dynamics in complex environments.
• The TENSO code provides a versatile tool for researchers in quantum dynamics and quantum information.
• This method opens possibilities for studying chemically complex quantum systems with structured baths.