Lattice Scalar Field Theory At Complex Coupling

Abstract

Lattice scalar field theories encounter a sign problem when the coupling constant is complex. This is a close cousin of the real-time sign problems that afflict the lattice Schwinger-Keldysh formalism, and a more distant relative of the fermion sign problem that plagues calculations of QCD at finite density. We demonstrate the methods of complex normalizing flows and contour deformations on scalar fields in $0+1$ and $1+1$ dimensions, respectively. In both cases, intractable sign problems are readily bypassed. These methods extend to negative couplings, where the partition function can be defined only by analytic continuation. Finally, we examine the location of partition function zeros, and discuss their relation to the performance of these algorithms.

arXiv comment9 pages, 6 figures

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Cited by in corpus (6)

• Exploring QCD matter in extreme conditions with Machine Learning
• Sampling the lattice Nambu-Goto string using Continuous Normalizing Flows
• Improving efficiency of the path optimization method for a gauge theory
• Deep Learning of Fermion Sign Fluctuations
• Coupling renormalization flow in the strongly interacting regime of an asymptotically free quantum field theory in four dimensions
• Convex optimization and contour deformations