Lattice Field Theory with theta-term and Renormalization Group

具有 theta 项和重正化群的格场论

• 批准号: 15540249
• 负责人: IMACHI Masahiro
• 金额: $ 1.34万
• 依托单位: Yamagata University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2003
• 资助国家: 日本
• 起止时间: 2003 至 2005
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-15540249/
• 关键词: Lattice Field Theory; CP^{N-1}; Theta term; Complex Boltzmann Factor; Maximum Entropy Method; Topological Charge Distribution; Pure Imaginary theta; Finite Density QCD; 複数ボルツマン因子; トポロジカル荷電; CP^N-1場の理論; フラットニング; 純虚数テータパラメータ; 数値実験; CP^<N-1>模型

We investigated the role of MEM (Maximum Entropy Method) on the problem of negative sign problem in the CP^{N-1} model with theta-term. Theta -dependence of free energy obtains non smooth behavior due to negative sign problem. This phenomena is called "flattening". In such case, MEM sometimes shows non-flat smooth behavior (M.Imachi, Y.Shinno and H.Yoneyama. Prog.Theor.Phys. {111} No.3 (2004)). Then there appears the question that whether MEM will give non-smooth behavior, insuch a case where physical data gives the first order phase transition. This problem is investigated in Nucl.Phys. (Proc.Suppl.) 140 (2005), 617-619 (Imachi, Shinno and Yoneyama).2)Azcoiti et al proposed the method to treat theta as pure imaginary. They applied the method to strong coupling region. We studied the weak coupling region of CP^{2} model. We used alpha chip PC's which are introduced by previous grant and notebook PC introduced in 2003 (2003.9.1 : note PC (CLEVO 400)) and two desktop PC's introduced in 2004 by grant (PC (H17.2.25, Desktop : Vip-HG 5330G/DVRDL, Vip-HG 5432P/DVRDL/GF66)). Numerical simulation is performed by these machines. We found stepwise behavior of free energy as a function of h (= imaginary part of theta). The property of imaginary theta is closely related to the problem of chemical potential in finite density QCD. Actually similar stepwise behavior is reported in finite density QCD studies e.g. by de Forcrand et al (Kratochvila and de Forcrand, hep-lat/0409072, hep-lat/0509143). Our result is summarised in a paper hep-lat/0601028, (by Imachi, Kmbayashi, Shinno and Yoneyama).

本文研究了最大熵方法在含θ项的CP^{N-1}模型中的负号问题中的作用。自由能的θ依赖性由于负符号问题而表现出非光滑性.这种现象被称为“扁平化”。在这种情况下，MEM有时显示非平坦平滑行为（M.Imachi，Y.Shinno和H. Yoneyama. Prog.Theor.Phys. {111} No. 3（2004））。于是就出现了这样一个问题，即在物理数据给出一阶相变的情况下，MEM是否会给出非光滑的行为。在Nucl.Phys.（Proc.Suppl.）140（2005），617-619（Imachi，Shinno和Yoneyama）。2）Azcoiti等人提出了将θ视为纯虚的方法。他们将该方法应用于强耦合区。研究了CP^{2}模型的弱耦合区.我们使用了由前一个格兰特公司推出的阿尔法芯片PC和2003年推出的笔记本电脑（2003.9.1：笔记本电脑（CLEVO 400））以及由格兰特公司于2004年推出的两台台式电脑（PC（H17.2.25，台式电脑：Vip-HG 5330 G/DVRDL，Vip-HG 5432 P/DVRDL/GF 66））。数值模拟由这些机器进行。我们发现逐步行为的自由能作为一个功能的h（=虚部θ）。虚θ的性质与有限密度QCD中的化学势问题密切相关。实际上，在有限密度QCD研究中，例如de Forcrand等人（Kratochvila和de Forcrand，hep-lat/0409072，hep-lat/0509143）报道了类似的逐步行为。我们的结果总结在一篇论文hep-lat/0601028中（由Imachi，Kmbayashi，Shinno和Yoneyama）。

项目成果

APPLICATION OF MAXIMUM ENTROPY METHOD TO LATTICE FIELD THEORY WITH A TOPOLOGICAL TERM

最大熵法在拓扑项格子场论中的应用

• 发表时间: 2004
• 期刊: Nucl.Phys.(Proc.Suppl.) 129
• 作者: M.Imachi;Y.Shinno;H.Yoneyama;S.Aoki;S.Aoki;井町昌弘;T.Kaneko;M.Imachi;T.Kaneko;M.Imachi
• 通讯作者: M.Imachi

MEM study of true flattening of free energy and the theta term

自由能真实平坦化和 theta 项的 MEM 研究

• 发表时间: 2005
• 期刊: Nucl. Phys. (Proc. Suppl.) 140
• 作者: S.Takeda;S.Aoki;et al.;S.Takeda;S.Aoki;S.Aoki;S.Takeda;井町昌弘
• 通讯作者: 井町昌弘

MAXIMUM ENTROPY METHOD APPROACH TO THETA TERM

Theta 项的最大熵方法

• 发表时间: 2004
• 期刊: Prog.Theor.Phys. 111・3
• 作者: S.Takeda;S.Aoki;et al.;M.Imachi
• 通讯作者: M.Imachi

M.Imachi他: "Maximal Entrogy Method Approach to the θ Term"Prog.Theor.Phys.. 111・3. (2004)

M. Imachi 等：“θ 项的最大熵方法”Prog.Theor.Phys.. 111・3。