In our previous paper [1], we found that the complex Langevin (CL) method works for QCD at finite density on the 163 × 32 lattice in the low-temperature high-density regime within the range μ/T = 1.6 – 9.6 with μ and T being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the 243 × 12 lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is L = (1.3 − 2.7 fm) > <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27400_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mtext>LQCD</mtext> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\Lambda}_{\textrm{LQCD}}^{-1} $</EquationSource> </InlineEquation> ∼ 1 fm, in contrast to our previous study with L < <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_27400_Article_IEq1.gif" Format="GIF" Height="24" Rendition="HTML" Resolution="72" Type="Linedraw" Width="47" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <msubsup> <mi mathvariant="normal">Λ</mi> <mtext>LQCD</mtext> <mrow> <mo>−</mo> <mn>1</mn> </mrow> </msubsup> </math></EquationSource> <EquationSource Format="TEX">$ {\Lambda}_{\textrm{LQCD}}^{-1} $</EquationSource> </InlineEquation>. We find that the CL method works in a broad region up to μ/T = 4.8, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.

On the validity of the complex Langevin method near the deconfining phase transition in QCD at finite density

期刊论文
出版模式：

开放获取
发表日期：

2025年10月14日

查看全文

Shoichiro Tsutsui,
Yuhma Asano,
Yuta Ito,
Hideo Matsufuru,
Yusuke Namekawa,
Jun Nishimura,
Shinji Shimasaki,
Asato Tsuchiya

摘要

In our previous paper [1], we found that the complex Langevin (CL) method works for QCD at finite density on the 16³ × 32 lattice in the low-temperature high-density regime within the range μ/T = 1.6 – 9.6 with μ and T being the quark chemical potential and the temperature, which enabled us to see a clear trend towards the formation of the Fermi sphere. Here we investigate the validity of the CL method on the 24³ × 12 lattice in the deconfined phase near the deconfinement phase transition. As before, we use four-flavor staggered fermions and judge the validity using the criterion based on the probability distribution of the drift term. The spatial extent is L = (1.3 − 2.7 fm) > $Λ_{LQCD}^{- 1}$ $ {\Lambda}_{\textrm{LQCD}}^{-1} $ ∼ 1 fm, in contrast to our previous study with L < $Λ_{LQCD}^{- 1}$ $ {\Lambda}_{\textrm{LQCD}}^{-1} $ . We find that the CL method works in a broad region up to μ/T = 4.8, while it starts to fail as we approach the phase boundary due to the singular drift problem, which can be understood qualitatively by extending the Banks-Casher relation to the case at finite density.