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arXiv · 1604.00956

Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles

Andrei Alexandru·Gokce Basar·Paulo F. Bedaque·Gregory W. Ridgway·Neill C. Warrington
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Abstract

A solution to the sign problem is the so-called "Lefschetz thimble approach" where the domain of integration for field variables in the path integral is deformed from the real axis to a sub-manifold in the complex space. For properly chosen sub-manifolds ("thimbles") the sign problem disappears or is drastically alleviated. The parametrization of the thimble by real coordinates require the calculation of a jacobian with a computational cost of order O(V^3), where V is proportional to the spacetime volume. In this note we propose two estimators for this jacobian with a computational cost of order O(V). We discuss analytically the regimes where we expect the estimator to work and show numerical examples in two different models.

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Andrei Alexandru, Gokce Basar, Paulo F. Bedaque, Gregory W. Ridgway, Neill C. Warrington. 2016-04-04. Fast Estimator of jacobians in Monte Carlo Integration on Lefschetz Thimbles. https://doi.org/10.1103/physrevd.93.094514

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