Piecewise interaction picture density matrix quantum Monte Carlo.

Area of Science:

• Computational Physics
• Quantum Chemistry
• Materials Science

Background:

• Density Matrix Quantum Monte Carlo (DMQMC) methods are crucial for stochastically sampling the exact N-body density matrix of interacting electrons.
• Current methods, like interaction picture DMQMC (IP-DMQMC), are limited to sampling only one inverse temperature point per calculation.
• This limitation necessitates multiple simulations to cover a temperature range, increasing computational expense.

Purpose of the Study:

• To introduce a modified IP-DMQMC method enabling the sampling of a temperature range within a single computational run.
• To reduce the overall computational cost associated with finite-temperature electronic structure calculations.
• To enhance the efficiency of quantum Monte Carlo simulations for interacting electron systems.

Main Methods:

• A modification to the interaction picture DMQMC (IP-DMQMC) algorithm is proposed.
• The method incorporates a change of picture away from the interaction picture upon reaching the target inverse temperature.
• Equations of motion utilize piecewise functions, combining interaction picture dynamics with the Bloch equation at the target temperature.

Main Results:

• The modified method successfully samples a range of inverse temperatures within a single simulation.
• Performance was evaluated across various molecular test systems.
• The new algorithm demonstrates comparable or superior performance to existing DMQMC and IP-DMQMC methods.

Conclusions:

• The developed method offers a significant computational advantage by enabling multi-temperature sampling in one go.
• This advancement streamlines finite-temperature electronic structure calculations.
• The improved efficiency makes it a valuable tool for studying interacting electron systems in computational physics and chemistry.