Stable recursive auxiliary field quantum Monte Carlo algorithm in the canonical ensemble: Applications to thermometry...

Area of Science:

• Quantum Many-Body Physics
• Statistical Mechanics
• Computational Physics

Background:

• Finite-sized interacting quantum systems are often described by the canonical ensemble.
• Conventional numerical methods face limitations in simulating these systems, such as approximations or poor scaling.

Purpose of the Study:

• Introduce a novel, stable auxiliary field quantum Monte Carlo method for direct canonical ensemble simulations.
• Apply this method to the fermion Hubbard model to address the sign problem and improve performance.
• Quantify the effects of excitations and analyze thermometry in ultracold atoms.

Main Methods:

• Developed a recursive auxiliary field quantum Monte Carlo approach.
• Simulated the fermion Hubbard model in 1D and 2D, including sign-problem regimes.
• Employed an estimator-agnostic approach to quantify excitations and compare density matrices.

Main Results:

• Achieved improved performance and rapid convergence to ground-state values for the fermion Hubbard model.
• Demonstrated the method's stability and effectiveness in canonical ensemble simulations.
• Identified potential underestimation of temperatures in ultracold atom thermometry using grand canonical ensemble analysis.

Conclusions:

• The new quantum Monte Carlo method provides a powerful tool for canonical ensemble simulations.
• The findings highlight limitations in current thermometry techniques for ultracold atoms.
• This work advances the simulation of quantum systems and understanding of thermodynamic properties.