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Taming the Dynamical Sign Problem in Real-Time Evolution of Quantum Many-Body Problems
Guy Cohen1,2, Emanuel Gull3, David R Reichman1
1Department of Chemistry, Columbia University, New York, New York 10027, USA.
Physical Review Letters
|January 15, 2016
Summary
A new inchworm algorithm significantly improves simulations of quantum dynamics by overcoming the dynamical sign problem. This method changes computational scaling from exponential to quadratic, enabling longer and more complex simulations.
Area of Science:
- Quantum mechanics
- Computational physics
Background:
- Nonequilibrium Monte Carlo methods face a dynamical sign problem.
- Simulating real-time quantum dynamics is computationally expensive and limited to short times.
Purpose of the Study:
- Introduce a novel algorithm to overcome the dynamical sign problem in quantum simulations.
- Enable efficient simulation of real-time quantum dynamics for extended periods.
Main Methods:
- Propose the "inchworm algorithm" that iteratively reuses previous simulation data.
- Apply the algorithm to the Anderson impurity model in Kondo and mixed valence regimes.
Main Results:
- The inchworm algorithm largely overcomes the dynamical sign problem.
- Computational scaling is reduced from exponential to quadratic.
- Successfully simulated quenches and spin dynamics under oscillatory magnetic fields.
Conclusions:
- The inchworm algorithm offers a significant advancement for simulating quantum many-body systems.
- Provides a more efficient and scalable approach to studying real-time quantum dynamics.
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