Flexible class of exact Hubbard-Stratonovich transformations

Area of Science:

• Condensed Matter Physics
• Computational Physics

Background:

• Hubbard interactions are crucial for understanding strongly correlated electron systems.
• Quantum Monte Carlo (QMC) simulations are powerful tools for studying these systems.
• The sign problem remains a significant challenge in QMC simulations of many-fermion systems.

Purpose of the Study:

• To develop and analyze a class of Hubbard-Stratonovich transformations for QMC.
• To investigate the impact of a tunable parameter on the sign problem.
• To explore the trade-offs between different sampling methods.

Main Methods:

• We propose a tunable Hubbard-Stratonovich transformation with parameter p.
• The transformation interpolates between discrete Ising and compact sinusoidal auxiliary fields.
• Numerical benchmarks were performed on single-band square and triangular Hubbard models.

Main Results:

• The severity of the sign problem systematically decreases as the parameter p increases.
• Finite values of p allow for the application of continuous sampling methods like Langevin or Hamiltonian Monte Carlo.
• Trade-offs between simulation methods were explored through numerical benchmarks.

Conclusions:

• The developed Hubbard-Stratonovich transformation offers a flexible approach to mitigate the sign problem in QMC.
• Increasing the parameter p is an effective strategy for reducing the sign problem.
• The choice of p allows for a balance between sign problem reduction and the applicability of continuous sampling techniques.