Convex optimization and contour deformations

Abstract

We discuss various formal aspects of contour deformations used to alleviate sign problems; most importantly, relating these contour deformations to a certain convex optimization problem. As a consequence of this connection we describe a general method for proving upper bounds on the average phase achievable by the contour deformation method. Using this method we show that Abelian lattice Yang-Mills in two spacetime dimensions possesses, for many values of the complex coupling, an exponential sign problem that cannot be removed via any contour deformation.

13 pages; version accepted to journal

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• Is it worth the effort to find Lefschetz thimbles? Integration contours with numerically optimal signal-to-noise ratios in simple fermionic toy models
• Path optimization method for the sign problem caused by fermion determinant