Lefschetz-thimble analysis of the sign problem in one-site fermion model
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Abstract
The Lefschetz-thimble approach to path integrals is applied to the one-site model of electron systems. Since the one-site Hubbard model shows a non-analytic behavior at the zero temperature and its path integral expression has the sign problem, this toy model is a good testing ground for various approaches to the sign problem. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles, and the non-analytic behavior turns out to be explained by this interference. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles.Keywords
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