Sign problem in finite density lattice QCD

Goy, V.A.; Bornyakov, V.; Boyda, D.; Molochkov, A.; Nakamura, A.; Nikolaev, A.; Zakharov, V.

doi:10.1093/ptep/ptx018

Sign problem in finite density lattice QCD

V.A. Goy
(
- Far Eastern Natl. U.
)
,
V. Bornyakov
(
- Far Eastern Natl. U. and
- Moscow, ITEP
)
,
D. Boyda
(
- Far Eastern Natl. U.
)
,
A. Molochkov
(
- Far Eastern Natl. U. and
- Moscow, ITEP
)
,
A. Nakamura
(
)

Nov 24, 2016

7 pages

Published in:

PTEP 2017 (2017) 3, 031D01

Published: Mar 1, 2017

e-Print:

1611.08093 [hep-lat]

DOI:

10.1093/ptep/ptx018

View in:

reference search33 citations

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Abstract: (Oxford University Press)

The canonical approach, which was developed for solving the sign problem, may suffer from a new type of sign problem. In this method, the grand partition function is written as a fugacity expansion:

Z_G(\mu,T) = \sum_n Z_C(n,T) \xi^n

, where

\xi=\exp(\mu/T)

is the fugacity, and

Z_C(n,T)

are given as averages over a Monte Carlo update,

\langle z_n\rangle

. We show that the complex phase of

z_n

is proportional to

n

at each Monte Carlo step. Although

\langle z_n\rangle

take real positive values, the values of

z_n

fluctuate rapidly when

n

is large, especially in the confinement phase, which gives a limit on

n

. We discuss a mechanism of phase emergence.

Note:

7 pages, 6 figures

D31
D34
D31 Quark-gluon plasma
D34 Lattice QCD calculations in nuclear physics
density: finite
potential: chemical
numerical calculations: Monte Carlo
quantum chromodynamics: lattice
partition function
fluctuation

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