Lefschetz-thimble flows without blow-up
Lefschetz-thimble method becomes a powerful tool to study the sign problem. It defines the steepest descent contours by the gradient flow in complexified field configurations. Solutions of the gradient flow, however, generically blow up in a finite time, and thus it must be solved with great cares.
We propose a new gradient flow without blow-ups that equally solves the sign problem as the conventional one does. We report its theoretical foundations and also its behaviors in numerical studies of simple examples.
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Nonzero Temperature and Density