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Optimal tree tensor network operators for tensor network simulations: Applications to open quantum systems.

Weitang Li1,2, Jiajun Ren3, Hengrui Yang4

  • 1School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen 518172, People's Republic of China.

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Summary
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This study introduces an efficient algorithm for constructing optimal tree tensor network operators (TTNO). This method enables accurate simulations of open quantum systems, demonstrating linear scaling computational cost.

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Area of Science:

  • Quantum mechanics
  • Computational physics
  • Condensed matter theory

Background:

  • Tree tensor network states (TTNS) are crucial for simulating complex quantum systems.
  • Existing methods for constructing tree tensor network operators (TTNO) can be computationally intensive.
  • Efficient simulation of open quantum systems is vital for understanding phenomena like spin relaxation and charge transport.

Purpose of the Study:

  • To develop an algorithm for automatic construction of optimal and exact tree tensor network operators (TTNO).
  • To apply the developed TTNO construction to simulate open quantum systems, including spin relaxation and charge transport.
  • To demonstrate the computational efficiency and scalability of the new approach.

Main Methods:

  • Algorithm based on the minimum vertex cover of a bipartite graph for optimal TTNO construction.
  • Simulation of open quantum systems using discrete environmental modes and the Cole-Davidson spectral density.
  • Incorporation of temperature effects using thermo-field dynamics.

Main Results:

  • Successful automatic construction of optimal and exact TTNO for sum-of-product quantum operators.
  • Accurate simulation of spin relaxation dynamics in the spin-boson model and charge transport in molecular junctions.
  • Demonstrated linear scaling of computational cost with the number of discretized environmental modes.

Conclusions:

  • The developed algorithm provides an efficient and exact method for constructing TTNO.
  • The approach enables accurate and scalable simulations of open quantum systems.
  • This work advances the simulation capabilities for complex quantum phenomena in condensed matter and molecular systems.