Controlling Complex Langevin simulations of lattice models by boundary term analysis

Scherzer, M.; Seiler, E.; Sexty, D.; Stamatescu, I.-O.

doi:10.1103/PhysRevD.101.014501

Controlling Complex Langevin simulations of lattice models by boundary term analysis

M. Scherzer
(
- U. Heidelberg, ITP
)
,
E. Seiler
(
- Munich, Max Planck Inst.
)
,
D. Sexty
(
- Wuppertal U. and
- ZAT, Julich
)
,
I.-O. Stamatescu
(
- U. Heidelberg, ITP
)

Oct 21, 2019

15 pages

Published in:

Phys.Rev.D 101 (2020) 1, 014501

Published: Jan 7, 2020

e-Print:

1910.09427 [hep-lat]

DOI:

10.1103/PhysRevD.101.014501

View in:

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Abstract: (APS)

One reason for the well-known fact that the complex Langevin (CL) method sometimes fails to converge or converges to the wrong limit has been identified long ago: it is insufficient decay of the probability density either near infinity or near poles of the drift, leading to boundary terms that spoil the formal argument for correctness. To gain a deeper understanding of this phenomenon, in a previous paper [Phys. Rev. D 99, 014512 (2019)PRVDAQ2470-001010.1103/PhysRevD.99.014512] we have studied the emergence of such boundary terms thoroughly in a simple model, where analytic results can be compared with numerics. Here we continue this type of analysis for more physically interesting models, focusing on the boundaries at infinity. We start with Abelian and non-Abelian one-plaquette models, and then we proceed to a Polyakov chain model and finally to high density QCD and the 3D XY model. We show that the direct estimation of the systematic error of the CL method using boundary terms is in principle possible.

Note:

17 pages, 11 figures

Lattice field theories, lattice QCD
model: lattice
Langevin equation: complex
quantum chromodynamics: density
density: high
boundary condition
nonabelian
XY model
dimension: 3
abelian

References(22)

Figures(30)

[1]

Complex Langevin and boundary terms

Manuel Scherzer
(
- U. Heidelberg, ITP
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Dénes Sexty
(
- Bergische U., Wuppertal (main) and
- IAS, Julich
)
,
Ion-Olimpiu Stamatescu
(
- U. Heidelberg, ITP
)

- Phys.Rev.D 99 (2019) 1, 014512
•
e-Print:
- 1808.05187
•
DOI:
- 10.1103/PhysRevD.99.014512

[2]

The Complex Langevin method: When can it be trusted?

Gert Aarts
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U.
)

- Phys.Rev.D 81 (2010) 054508
•
e-Print:
- 0912.3360
•
DOI:
- 10.1103/PhysRevD.81.054508

[3]

Complex Langevin: Etiology and Diagnostics of its Main Problem

Gert Aarts
(
- Swansea U.
)
,
Frank A. James
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U. and
- Heidelberg, FEST
)

- Eur.Phys.J.C 71 (2011) 1756
•
e-Print:
- 1101.3270
•
DOI:
- 10.1140/epjc/s10052-011-1756-5

[4]

Status of Complex Langevin

Erhard Seiler
(
- Munich, Max Planck Inst.
)

- EPJ Web Conf. 175 (2018) 01019
•
e-Print:
- 1708.08254
•
DOI:
- 10.1051/epjconf/201817501019

[5]

Localised distributions and criteria for correctness in complex Langevin dynamics

Gert Aarts
(
- Swansea U.
)
,
Pietro Giudice
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)

- Annals Phys. 337 (2013) 238-260
•
e-Print:
- 1306.3075
•
DOI:
- 10.1016/j.aop.2013.06.019

[6]

Gauge cooling in complex Langevin for QCD with heavy quarks

Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Denes Sexty
(
- Heidelberg U.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U.
)

- Phys.Lett.B 723 (2013) 213-216
•
e-Print:
- 1211.3709
•
DOI:
- 10.1016/j.physletb.2013.04.062

[7]

Stability of complex Langevin dynamics in effective models

Gert Aarts
(
- Swansea U.
)
,
Frank A. James
(
- Regensburg U.
)
,
Jan M. Pawlowski
(
- Heidelberg U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Denes Sexty
(
- Heidelberg U.
)

et al.

- JHEP 03 (2013) 073
•
e-Print:
- 1212.5231
•
DOI:
- 10.1007/JHEP03(2013)073

[8]

Full QCD and QED at finite temperature and chemical potential

I. Bender
(
- Heidelberg U.
)
,
T. Hashimoto
(
- Fukui U.
)
,
F. Karsch
(
- Bielefeld U. and
- Julich, NIC
)
,
V. Linke
(
- Freie U., Berlin
)
,
A. Nakamura
(
- Heidelberg U. and
- Heidelberg, FEST
)

et al.

- Nucl.Phys.B Proc.Suppl. 26 (1992) 323-325,
- Tsukuba Lattice 1991:323-325
•
DOI:
- 10.1016/0920-5632(92)90265-T

[9]

High density QCD with static quarks

- Phys.Rev.Lett. 76 (1996) 1019-1022
•
e-Print:
- hep-lat/9509002
•
DOI:
- 10.1103/PhysRevLett.76.1019

[10]

A Model for QCD at high density and large quark mass

Roberto De Pietri
(
- Parma U. and
- INFN, Parma
)
,
Alessandra Feo
(
- Parma U. and
- INFN, Parma
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg, FEST and
- Heidelberg U.
)

- Phys.Rev.D 76 (2007) 114501
•
e-Print:
- 0705.3420
•
DOI:
- 10.1103/PhysRevD.76.114501

[11]

Heavy dense QCD and nuclear matter from an effective lattice theory

- JHEP 09 (2014) 131
•
e-Print:
- 1403.4162
•
DOI:
- 10.1007/JHEP09(2014)131

[12]

Simulating QCD at nonzero baryon density to all orders in the hopping parameter expansion

Gert Aarts
(
- Swansea U.
)
,
Erhard Seiler
(
- Munich, Max Planck Inst.
)
,
Dénes Sexty
(
- Heidelberg U.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U.
)

- Phys.Rev.D 90 (2014) 11, 114505
•
e-Print:
- 1408.3770
•
DOI:
- 10.1103/PhysRevD.90.114505

[13]

QCD in the heavy dense regime for general N $_{c}$ : on the existence of quarkyonic matter

Owe Philipsen
(
- Frankfurt U.
)
,
Jonas Scheunert
(
- Frankfurt U.
)

- JHEP 11 (2019) 022
•
e-Print:
- 1908.03136
•
DOI:
- 10.1007/JHEP11(2019)022

[14]

Stochastic quantization at finite chemical potential

Gert Aarts
(
- Swansea U.
)
,
Ion-Olimpiu Stamatescu
(
- Heidelberg U. and
- Heidelberg, FEST
)

- JHEP 09 (2008) 018
•
e-Print:
- 0807.1597
•
DOI:
- 10.1088/1126-6708/2008/09/018

[15]

The QCD phase diagram in the limit of heavy quarks using complex Langevin dynamics

Gert Aarts
(
- Swansea U.
)
,
Felipe Attanasio
(
- Swansea U.
)
,
Benjamin Jäger
(
- Swansea U.
)
,
Dénes Sexty
(
- Eotvos Lorand U., Budapest, Inst. Theor. Phys. and
- Bergische U., Wuppertal (main)
)

- JHEP 09 (2016) 087
•
e-Print:
- 1606.05561
•
DOI:
- 10.1007/JHEP09(2016)087

[16]

LANGEVIN SIMULATION INCLUDING DYNAMICAL QUARK LOOPS

A. Ukawa
(
- Tsukuba U.
)
,
M. Fukugita
(
- Kyoto U., Yukawa Inst., Kyoto
)

- Phys.Rev.Lett. 55 (1985) 1854,
- IN *DAMGAARD, P.H. (ED.), HUEFFEL, H. (ED.): STOCHASTIC QUANTIZATION*, 481-484. (PHYS. REV. LETT. 55 (1985) 1854-1857) AND TSUKUBA UNIV. - UTHEP-133 (85,REC.APR.) 14 P. (SEE BOOK INDEX)
•
DOI:
- 10.1103/PhysRevLett.55.1854