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Area of Science:

  • Quantum Many-Body Physics
  • Computational Physics

Background:

  • Non-Hermitian (NH) quantum systems present unique phenomena like NH skin effects and exceptional points.
  • Existing numerical methods struggle to analyze these complex systems.

Purpose of the Study:

  • To develop and apply novel computational techniques for investigating ground-state properties of NH quantum many-body systems.
  • To overcome the breakdown of the Rayleigh-Ritz variational principle in NH settings.

Main Methods:

  • Utilized variational Monte Carlo and neural network wave function representations.
  • Developed a self-consistent symmetric optimization framework based on variance minimization.
  • Incorporated biorthogonal structure, system symmetries, and pseudo-Hermiticity.

Main Results:

  • Accurately computed NH physical observables for a 2D transverse-field Ising model with a complex longitudinal field.
  • Successfully analyzed both parity-time symmetric and broken phases.
  • Demonstrated the method's scalability and flexibility.

Conclusions:

  • The developed method provides a powerful tool for studying NH quantum many-body systems.
  • This approach extends beyond the capabilities of conventional techniques like density-matrix renormalization group.
  • Offers a scalable and flexible computational solution for complex quantum simulations.