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Area of Science:

  • Quantum Information Science
  • Condensed Matter Physics
  • Machine Learning Applications

Background:

  • Open quantum systems exhibit complex dynamics crucial for understanding relaxation and phase transitions.
  • Characterizing these dynamics often requires calculating the Liouvillian gap, a computationally challenging task.

Purpose of the Study:

  • To introduce a novel machine learning-inspired variational method for efficiently determining the Liouvillian gap.
  • To demonstrate the method's applicability to complex quantum models like the dissipative Heisenberg model.

Main Methods:

  • Utilized a "spin bi-base mapping" to represent the density matrix as a restricted Boltzmann machine (RBM) state.
  • Transformed the Liouvillian superoperator into a rank-two non-Hermitian operator.
  • Employed a variational real-time evolution algorithm to compute the Liouvillian gap.

Main Results:

  • Successfully applied the RBM approach to the 1D and 2D dissipative Heisenberg models.
  • Achieved accurate results for the Liouvillian gap, validated against analytical solutions (including Bethe ansatz for 1D).
  • Demonstrated the method's efficiency and accuracy across different dimensions and entanglement properties.

Conclusions:

  • The proposed RBM-based variational method provides an efficient and accurate way to access the Liouvillian gap.
  • This technique offers a powerful tool for studying open quantum systems, relaxation dynamics, and dissipative phase transitions.