Biorthogonal Neural Network Approach to 2D Non-Hermitian Systems

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.