Interaction picture density matrix quantum Monte Carlo

Area of Science:

• Quantum Many-Body Physics
• Computational Quantum Chemistry

Background:

• The density matrix quantum Monte Carlo (DMQMC) algorithm enables exact sampling of the N-body thermal density matrix.
• Accessing exact properties of quantum systems at arbitrary temperatures is crucial for understanding material behavior.

Purpose of the Study:

• To demonstrate the benefits of using the interaction picture within the DMQMC algorithm for interacting fermions.
• To investigate and extrapolate basis set incompleteness error at finite temperatures.
• To perform benchmark calculations for the uniform electron gas in the warm dense regime.

Main Methods:

• Stochastic sampling of the N-body thermal density matrix using DMQMC.
• Application of the interaction picture to interacting fermion systems.
• Monte Carlo sampling for basis set incompleteness error extrapolation.
• Benchmark calculations for a four-electron system.

Main Results:

• The interaction picture offers substantial advantages for DMQMC applied to interacting fermions.
• Basis set incompleteness error at finite temperatures can be investigated and extrapolated.
• Benchmark results for a four-electron system are provided.

Conclusions:

• The DMQMC algorithm, particularly with the interaction picture, is a powerful tool for studying interacting fermions.
• Accurate calculations for systems like the warm dense electron gas are achievable.
• The methodology provides a foundation for future studies on complex quantum systems.