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We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.ĪB - The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. Analyzing such singular behaviors semiclassically, we propose a criterion to identify the necessary number of Lefschetz thimbles. If the number of Lefschetz thimbles is insufficient, we found not only large discrepancies from the exact result, but also thermodynamic instabilities. Semiclassical analysis using complex saddle points unveils the significance of interference among multiple Lefschetz thimbles to reproduce the non-analytic behavior by using the path integral. 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 an idea or a technique to attack the sign problem. N2 - The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. © 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft. T1 - Lefschetz-thimble analysis of the sign problem in one-site fermion model We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.",

Abstract = "The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model.