Abstract
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.
| Original language | English |
|---|---|
| Pages (from-to) | 94-105 |
| Number of pages | 12 |
| Journal | Nuclear Physics B |
| Volume | 911 |
| DOIs | |
| Publication status | Published - 2016 Oct 1 |
| Externally published | Yes |
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ASJC Scopus subject areas
- Nuclear and High Energy Physics
Cite this
Complex saddle points and the sign problem in complex Langevin simulation. / Hayata, Tomoya; Hidaka, Yoshimasa; Tanizaki, Yuya.
In: Nuclear Physics B, Vol. 911, 01.10.2016, p. 94-105.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Complex saddle points and the sign problem in complex Langevin simulation
AU - Hayata, Tomoya
AU - Hidaka, Yoshimasa
AU - Tanizaki, Yuya
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.
UR - http://www.scopus.com/inward/record.url?scp=84982787949&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84982787949&partnerID=8YFLogxK
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 -