Lefschetz-thimble analysis of the sign problem in one-site fermion model

Tanizaki, Yuya (Department of Physics, The University of Tokyo, Tokyo 113-0033, Japan) (Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan) (Author to whom any correspondence should be addressed., Japan) ; Hidaka, Yoshimasa (Theoretical Research Division, Nishina Center, RIKEN, Wako, Saitama 351-0198, Japan) ; Hayata, Tomoya (RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan)

01 March 2016

Abstract: The Lefschetz-thimble approach to path integrals is applied to a one-site model of electrons, i.e., the one-site Hubbard model. 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. 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. 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. We argue that this interference of multiple saddle points is a key issue to understand the sign problem of the finite-density quantum chromodynamics.

Published in: New J. Phys. 18 (2016) 033002
Published by: Institute of Physics Publishing/Deutsche Physikalische Gesellschaft
DOI: 10.1088/1367-2630/18/3/033002
arXiv: 1509.07146
License: CC-BY-3.0

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