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Infinite variance in fermion quantum Monte Carlo calculations
1Department of Physics, The College of William and Mary, Williamsburg, Virginia 23187, USA.
Physical Review. E
|April 15, 2016
Summary
Quantum Monte Carlo (QMC) methods solve many-fermion problems without the sign problem, but common algorithms suffer from infinite variance. A new approach using a "bridge link" corrects this, ensuring reliable calculations for condensed matter and physics models.
Area of Science:
- Physics
- Computational Physics
- Quantum Mechanics
Background:
- Quantum Monte Carlo (QMC) methods are crucial for solving many-fermion problems across condensed matter, nuclear, and high-energy physics.
- Many important models, such as the Hubbard model and lattice quantum chromodynamics, are now solvable without the sign problem using QMC.
Purpose of the Study:
- To identify and address the infinite variance problem in commonly used QMC algorithms.
- To propose a general solution that ensures the reliability of QMC calculations for sign-problem-free models.
Main Methods:
- Analysis of QMC algorithms to pinpoint the source of infinite variance.
- Introduction of a "bridge link" modification to the imaginary-time path integral in QMC algorithms.
Main Results:
- Demonstration that standard QMC algorithms can suffer from infinite variance, leading to unreliable statistical error bars.
- Validation of the proposed "bridge link" method through application to the Hubbard model at half-filling.
Conclusions:
- The infinite variance problem in QMC can compromise the accuracy of results for fundamental physics models.
- The proposed "bridge link" solution offers a robust and broadly applicable method to ensure the reliability of QMC calculations.
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