TY - JOUR

T1 - Lefschetz-thimble analysis of the sign problem in one-site fermion model

AU - Tanizaki, Yuya

AU - Hidaka, Yoshimasa

AU - Hayata, Tomoya

N1 - Publisher Copyright:
© 2016 IOP Publishing Ltd and Deutsche Physikalische Gesellschaft.

PY - 2016/3/1

Y1 - 2016/3/1

N2 - 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.

AB - 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.

KW - Lee-Yang zeros

KW - Lefschetz thimbles

KW - semiclassical analysis

KW - sign problem

UR - http://www.scopus.com/inward/record.url?scp=84960858910&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84960858910&partnerID=8YFLogxK

U2 - 10.1088/1367-2630/18/3/033002

DO - 10.1088/1367-2630/18/3/033002

M3 - Article

AN - SCOPUS:84960858910

SN - 1367-2630

VL - 18

JO - New Journal of Physics

JF - New Journal of Physics

IS - 3

M1 - 033002

ER -