Approximation for discrete Fourier transform and application in study of three-dimensional interacting electron gas

Area of Science:

• Computational physics
• Quantum mechanics
• Numerical analysis

Background:

• The discrete Fourier transform (DFT) is crucial for analyzing periodic data.
• Traditional DFT methods require substantial computational resources.
• Efficient approximations are needed for complex many-body systems.

Purpose of the Study:

• To develop and validate an approximation for the discrete Fourier transform.
• To enhance computational efficiency and reduce memory requirements for numerical calculations.
• To apply the approximation to a challenging problem in condensed matter physics.

Main Methods:

• Approximating the discrete Fourier transform by summing a subset of terms with weights.
• Applying the approximation to the three-dimensional interacting electron gas model.
• Utilizing the renormalized-ring-diagram approximation for self-consistent Green's function calculations.

Main Results:

• The approximation significantly improves computational efficiency and reduces memory usage.
• Accurate results were obtained for the chemical potential, compressibility, free energy, entropy, and specific heat.
• Ground-state energy calculations show good agreement with Monte Carlo and random-phase approximation methods.

Conclusions:

• The developed discrete Fourier transform approximation offers a powerful tool for large-scale numerical simulations.
• This method provides a computationally feasible approach for studying complex quantum systems.
• The enhanced efficiency allows for more in-depth analysis of condensed matter phenomena.