Gradient flows without blow-up for Lefschetz thimbles

Abstract

We propose new gradient flows that define Lefschetz thimbles and do not blow up in a finite flow time. We study analytic properties of these gradient flows, and confirm them by numerical tests in simple examples.

31 pages, 11 figures, (v2) conclusion part is expanded

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• Quantum tunnelling, real-time dynamics and Picard-Lefschetz thimbles
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• Reweighting Lefschetz Thimbles
• Mitigating the Hubbard Sign Problem with Complex-Valued Neural Networks
• On the gauge invariant path-integral measure for the overlap Weyl fermions in $\underline{16}$ of SO(10)
• Why is the mission impossible? -- Decoupling the mirror Ginsparg-Wilson fermions in the lattice models for two-dimensional abelian chiral gauge theories
• Complex complex landscapes
• Lefschetz Thimble Quantum Monte Carlo for Spin Systems
• The small-$N$ series in the zero-dimensional $O(N)$ model: constructive expansions and transseries
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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