TY - JOUR

T1 - Complex saddle points and the sign problem in complex Langevin simulation

AU - Hayata, Tomoya

AU - Hidaka, Yoshimasa

AU - Tanizaki, Yuya

N1 - Funding Information:
T.H. thanks A. Yamamoto for stimulating discussions. Y.T. was supported by Grants-in-Aid for the fellowship of Japan Society for the Promotion of Science ( JSPS ) (No. 25-6615 ) when he belonged to the University of Tokyo, and is supported by Special Postdoctoral Researchers Program of RIKEN . Y.H. is partially supported by JSPS KAKENHI Grants Numbers 15H03652 . This work was partially supported by the RIKEN interdisciplinary Theoretical Science (iTHES) project, and by the Program for Leading Graduate Schools of Ministry of Education, Culture, Sports, Science, and Technology ( MEXT ), Japan.
Publisher Copyright:
© 2016 The Author(s)

PY - 2016/10/1

Y1 - 2016/10/1

N2 - We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.

AB - We show that complex Langevin simulation converges to a wrong result within the semiclassical analysis, by relating it to the Lefschetz-thimble path integral, when the path-integral weight has different phases among dominant complex saddle points. Equilibrium solution of the complex Langevin equation forms local distributions around complex saddle points. Its ensemble average approximately becomes a direct sum of the average in each local distribution, where relative phases among them are dropped. We propose that by taking these phases into account through reweighting, we can solve the wrong convergence problem. However, this prescription may lead to a recurrence of the sign problem in the complex Langevin method for quantum many-body systems.

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U2 - 10.1016/j.nuclphysb.2016.07.031

DO - 10.1016/j.nuclphysb.2016.07.031

M3 - Article

AN - SCOPUS:84982787949

VL - 911

SP - 94

EP - 105

JO - Nuclear Physics B

JF - Nuclear Physics B

SN - 0550-3213

ER -