Journal
PHYSICAL REVIEW LETTERS
Volume 117, Issue 8, Pages -Publisher
AMER PHYSICAL SOC
DOI: 10.1103/PhysRevLett.117.081602
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Funding
- National Science Foundation CAREER [PHY-1151648]
- U.S. Department of Energy [DE-FG02-93ER-40762]
- Division Of Physics
- Direct For Mathematical & Physical Scien [1151648] Funding Source: National Science Foundation
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Monte Carlo studies involving real time dynamics are severely restricted by the sign problem that emerges from a highly oscillatory phase of the path integral. In this Letter, we present a new method to compute real time quantities on the lattice using the Schwinger-Keldysh formalism via Monte Carlo simulations. The key idea is to deform the path integration domain to a complex manifold where the phase oscillations are mild and the sign problem is manageable. We use the previously introduced contraction algorithm to create a Markov chain on this alternative manifold. We substantiate our approach by analyzing the quantum mechanical anharmonic oscillator. Our results are in agreement with the exact ones obtained by diagonalization of the Hamiltonian. The method we introduce is generic and, in principle, applicable to quantum field theory albeit very slow. We discuss some possible improvements that should speed up the algorithm.
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