夸克介子模型的相图和表面张力

利用有限温度场论和平均场近似的方法,在考虑夸克真空涨落的情况下,研究了两个夸克味的夸克介子模型的量子色动力学相变的相图结构,得到了当夸克化学势密度较小时,量子色动力学相变是过渡相变,而当夸克化学势密度较大的时候,量子色动力学相变是一级相变.对于一级相变的区域,基于薄壁近似,给出了当温度等于临界温度Tc时,强子相表面张力随夸克化学势密度的变化关系.本研究为相对论重离子对撞实验和中子星早期结构演化提供必要的参考.     

基态八重态重子质量的手征描述

质量作为物质最基本的属性,其起源一直是物理学研究的根本问题之一。根据物质层次的 划分,理解可见宇宙物质（能量）组成的关键在于理解核子（基态重子）的质量。现代粒子物理与 原子核物理研究指出,基态重子质量的绝大部分来自强相互作用。然而,由于色禁闭现象,强相互 作用的基本理论–量子色动力学–在低能区无法解析求解,导致很长一段时间里对基态重子质量的 研究不得不借助于各种唯象模型。二十一世纪以来,随着计算机运算能力的发展和算法的持续改 进,格点量子色动力学模拟取得了令人瞩目的成绩,使得人类从第一原理出发计算基态重子的质 量,进而定量地理解质量的起源成为可能。另一方面,受到计算资源的限制,目前绝大部分格点 量子色动力学模拟必须采用比物理值大的轻夸克质量、不足够大的盒子体积和不足够小的格点间 距。因而,为了从格点量子色动力学模拟中提取感兴趣的观测量的物理值,必须对格点数据进行 如下三种延拓：手征延拓将轻夸克质量延拓到物理值（即mq ! mphys: q ）,有限体积修正将有限的四 维空间延拓到无穷大（即V = L4 ! 1）,连续性延拓将有限格点间距延拓到零（即a ! 0）。手征 微扰理论为开展这些延拓提供了必要的理论基础。作为量子色动力学的低能有效理论,手征微扰 理论原则上可以模型无关地描述强相互作用物理。但随着手征阶数的升高,仅仅依靠实验数据无 法完全确定理论中未知的低能常数。高统计量的格点量子色动力学模拟数据的出现为解决这一难 题提供了新的思路,从而使得基于高阶手征微扰理论的研究成为可能。本文将简要介绍当前基于 协变重子手征微扰理论对基态八重态重子质量及格点量子色动力学模拟数据的研究。     

海森堡J1-J2自旋链的量子关联与量子纠缠

文章计算了海森堡J1-J2自旋链的任意两格点间的量子失谐与相对熵纠缠,不仅给出了量子失谐、相对熵纠缠与两格点自旋关联函数的解析关系,而且给出了精确对角化的数值结果.解析结果指出了两格点的量子失谐与纠缠非零的条件,并为用两格点的量子失谐与纠缠探测该模型的相变点提供了理论依据.数值结果表明,在该模型中,量子失谐比纠缠具有较长程的关联,近邻和远距离两格点间的量子失谐在基态时能标度一级相变点J2/J1 =0.5,在第一激发态时,除了能标度相变点J2/J1=0.5外,还能标度无穷级相变点J2/J1 =0.241 1;而纠缠仅存在最近邻与次近邻两格点间,且只有最近邻两格点的纠缠能标度相变点.     

一维伊辛模型的相变-Ⅱ

找到了一个能够用矩阵法计算的新序参量,此参量既能给出有限数量格点时一维伊辛模型中存在相变,又能给出无限数量格点时相变消失的结果.利用此序参量求出了一个计算相变点的简洁近似公式.     

基于投影纠缠对态算法优化的研究

二维强关联电子量子格点系统的投影纠缠对态(PEPS)算法是数值计算领域中研究二维强关联电子量子格点系统最为重要的张量网络算法.基于PEPS算法研究二维量子XYX模型与二维量子Ising模型,本文对PEPS算法进行了一些优化和改进研究,这些优化和改进主要体现在如何进行PEPS张量的更新与如何进行物理观测量的计算这两个方面,从而可以大大提高计算资源的利用.因而优化和改进后的PEPS算法可为研究热力学极限下的二维强关联电子量子格点系统的量子相变和量子临界现象提供一种更有效的强大的工具.     

一维自旋1键交替XXZ链中的量子纠缠和临界指数

利用基于张量网络表示的矩阵乘积态算法以及无限虚时间演化块抽取方法,本文研究了一维无限格点自旋1的键交替反铁磁XXZ海森伯模型中的量子相变.分别计算了系统的von Neumann熵、单位格点保真度和序参量,从而得到了系统随键交替强度的变化从拓扑有序Néel相到局域有序二聚化相的量子相变点.我们用矩阵乘积态方法拟合出了相变的中心荷c?0.5,表明此相变属于二维经典的Ising普适类.另外,通过对拓扑Néel序的数值拟合,我们得到了相变点处的特征临界指数β′=0.236和γ′=0.838.     

同位旋非对称强作用物质状态方程及热力学性质

在Nambu-Jona-Lasinio模型框架下,研究温度和重子化学势对同位旋非对称量子色动力学物质状态方程和热力学性质的影响.通过将零温和零重子化学势下的pion超流物质状态方程以及有限温下同位旋密度、压强与格点数据做比较,发现两种方法给出的结果符合得较好.进一步计算表明,零温和零重子化学势下的平均同位旋能量随同位旋密度单调增加,而非零重子化学势和有限温下却呈现具有极小值的非对称抛物线行为.最后,利用得到的状态方程探讨声速随同位旋化学势的变化行为,结果显示有限温和(或)重子化学势下的声速在相变点不连续,且超流相中的声速饱和值明显大于普通核物质及夸克物质中的值.另外,在超流相中重子化学势和温度具有软化状态方程以及降低声速的作用.     

基于深度学习的两分量BEC中量子相变点的识别

识别物质的相变是物理学研究中一个重要问题.本文采用了一种混淆标签方案的卷积神经网络算法来识别两分量玻色-爱因斯坦凝聚(BEC)中量子相变点,通过计算神经网络输出的准确率,得到W型性能曲线,此性能曲线中间的极大值对应着量子相变的临界点.研究结果表明,深度学习得到的量子相变点与解析计算值吻合度较高.此混淆标签方案的深度学习研究方法可以应用到存在两种相的相变体系.     

Ising模型的并行计算

以Ising模型为例,介绍有关格点系统的Monte Carlo数值模拟并行算法的设计和编程,并给出在本组建造的PC集群式高性能并行计算系统上的测量结果.本文的结果对格点量子色动力学的大规模数值模拟研究有一定的参考价值     

利用格点量子色动力学研究手征平滑过渡温度和手征相变温度

回顾了最近关于手征平滑过渡温度和手征相变温度的研究结果。首先给出了在零重子化学势能下的手征平滑过渡温度为156.5(1.5) MeV，其次，给出了在非零重子化学势能下手征相转变曲线的二阶及四阶曲率分别为0.012(4)和0.000(4)。接着讨论了在格点QCD中第一次得到的量子色动力学的手征相变温度。在热力学极限、连续极限及手征极限下，我们得到手征相变温度为132$^{+3}_{-6}$ MeV。     

Phase transition and the nucleon as a soliton in the Nambu-Jona-Lasinio model at finite temperature and density

We study some bulk thermodynamical characteristics, meson properties and the nucleon as a baryon-number-one soliton in hot quark matter in the NJL model as well as in hot nucleon matter in a hybrid NJL model in which the Dirac sea of quarks is combined with a Fermi sea of nucleons. In both cases, working in the mean-field approximation, we find a chiral phase transition from the Goldstone to the Wigner phase. At finite density the chiral order parameter and the constituent quark mass have a non-monotonic temperature dependence — at finite temperatures not close to the critical one they are less affected than in cold matter. Whereas quark matter is rather soft against thermal fluctuations and the corresponding chiral phase transition is smooth, nucleon matter is much stiffer and the chiral phase transition is very sharp. The thermodynamical variables show large discontinuities which is an indication for a first-order phase transition. We solve the B = 1 solitonic sector of the NJL model in the presence of external hot quark and nucleon media. In the hot medium at intermediate temperature the soliton is more bound and less swelled than in the case of cold matter. At some critical temperature, which for nucleon matter coincides with the critical temperature for the chiral phase transition, we find no more a localized solution. According to this model scenario one should expect a sharp phase transition from nucleon to quark matter.     

Quantum correlations in the dimerized spin chain at zero and finite temperatures

By using the method of exact diagonalization, we investigate the quantum correlation measured by quantum discord of the dimerized spin chain at both zero and finite temperatures. The results disclose that the quantum discord is robust at any finite parameter α and temperature T, in contrast to entanglement which shows a sudden death when the parameter α or the temperature T reaches a critical point. At finite temperature, it is interesting to find that the quantum discord QD _{2i−1, 2i} can increase with temperature T no matter if the entanglement EoF _{2i−1, 2i} exists or not. The research on the relation between the quantum discord and the quantum phase transition in the dimerized spin chain indicates that the transition can be characterized by the first derivation of the quantum discord at zero and low temperatures.     

Chiral phase transition at finite temperature in the linear sigma model

We study the chiral phase transition at finite temperature in the linear sigma model by employing a self-consistent Hartree approximation. This approximation is introduced by imposing self-consistency conditions on the effective meson mass equations which are derived from the finite temperature one-loop effective potential. It is shown that in the limit of vanishing pion mass, namely when the chiral symmetry is exact, the phase transition becomes a weak first order accompanying a gap in the order parameter as a function of temperature. This is caused by the long range fluctuations of meson fields whose effective masses become small in the transition region. It is shown, however, that with an explicit chiral symmetry breaking term in the Lagrangian which generates the realistic finite pion mass the transition is smoothed out irrespective of the choice of coupling strength. Recieved: 19 September 1997 / Revised version: 30 October 1997     

Quark potential in a quark–meson plasma

We investigate the effect of the restoration of chiral symmetry on the quark potential in a quark–meson plasma by considering meson exchanges in the two flavor Nambu–Jona-Lasinio model at finite temperature and density. There are two possible oscillations in the chiral restoration phase; one is the Friedel oscillation due to the sharp quark Fermi surface at high density, and the other is the Yukawa oscillation driven by the complex meson poles at high temperature. The quark–meson plasma is strongly coupled in the temperature region 1≤T/T _c≤3, with T _c being the critical temperature of the chiral phase transition. The maximum coupling in this region is located at the phase transition point.     

QCD with two colors at finite baryon density at next-to-leading order

We study QCD with two colors and quarks in the fundamental representation at finite baryon density in the limit of light-quark masses. In this limit the free energy of this theory reduces to the free energy of a chiral Lagrangian which is based on the symmetries of the microscopic theory. In earlier work this Lagrangian was analyzed at the mean-field level and a phase transition to a phase of condensed diquarks was found at a chemical potential of half the diquark mass (which is equal to the pion mass). In this article we analyze this theory at next-to-leading order in chiral perturbation theory. We show that the theory is renormalizable and calculate the next-to-leading order free energy in both phases of the theory. By deriving a Landau–Ginzburg theory for the order parameter we show that the finite one-loop contribution and the next-to-leading order terms in the chiral Lagrangian do not qualitatively change the phase transition. In particular, the critical chemical potential is equal to half the next-to-leading order pion mass, and the phase transition is of second order.     

On the phase structure of QCD in a finite volume

The chiral phase transition in QCD at finite chemical potential and temperature can be characterized for small chemical potential by its curvature and the transition temperature. The curvature is accessible to QCD lattice simulations, which are always performed at finite pion masses and in finite simulation volumes. We investigate the effect of a finite volume on the curvature of the chiral phase transition line. We use functional renormalization group methods with a two flavor quark-meson model to obtain the effective action in a finite volume, including both quark and meson fluctuation effects. Depending on the chosen boundary conditions and the pion mass, we find pronounced finite-volume effects. For periodic quark boundary conditions in spatial directions, we observe a decrease in the curvature in intermediate volume sizes, which we interpret in terms of finite-volume quark effects. Our results have implications for the phase structure of QCD in a finite volume, where the location of a possible critical endpoint might be shifted compared to the infinite-volume case.     

Phase transitions in quark matter and behaviour of physical observables in the vicinity of the critical end point

We study the chiral phase transition at finite T and μ _B within the framework of the SU(3) Nambu-Jona-Lasinio (NJL) model. The QCD critical end point (CEP) and the critical line at finite temperature and baryonic chemical potential are investigated: the study of physical quantities, such as the baryon number susceptibility near the CEP, will provide complementary information concerning the order of the phase transition. We also analyze the information provided by the study of the critical exponents around the CEP.     

The extended quark sigma model at finite temperature and baryonic chemical potential

An extended quark sigma model which includes higher-order mesonic interactions is studied at the finite baryonic chemical potential u _B and temperature T. The field equations have been solved in the mean-field approximation by using the modified iteration method at finite baryonic chemical potential u _B and temperature T. The Goldstone theorem is satisfied below a critical temperature in the chiral limit for u _B = 0. As expected from general universality, the chiral phase transition is second-order. By including the higher-order mesonic interactions, the critical temperature is reduced compared to that found in recent works and is in good agreement with lattice QCD results. The nucleon mass is examined in the (u _B , T) plane, showing a strong dependence on u _B and T. We find that an increase in both the baryonic chemical potential u _B and the temperature T leads to an increase in the values of the nucleon mass. This is evidence for the quark-gluon deconfinement phase transition at higher values of temperature.     

Critical phenomena with convergent series expansions in a finite volume

Linked cluster expansions are generalized from an infinite to a finite volume. They are performed to 20th order in the expansion parameter to approach the critical region from the symmetric phase. A new criterion is proposed to distinguish first- from second-order transitions within a finite-size scaling analysis. The criterion applies also to other methods for investigating the phase structure, such as Monte Carlo simulations. Our computational tools are illustrated with the example of scalar (O(N) models with four- and six-point couplings forN=1 andN=4 in three dimensions. It is shown how to localize the tricritical line in these models. We indicate some further applications of our methods to the electroweak transition as well as to models for superconductivity.     

Saturation of QCD ward identities above theSU(L)⊗SU(L) chiral transition

We discuss an effective Lagrangian model in which theU (1) chiral symmetry is restored above theSU (L) SU (L) chiral phase transition (L being the number of light flavours) and the topological susceptibilityX _YM of the pure Yang-Mills theory drops to zero above the chiral transition. A new order parameter is introduced for theU(1) chiral symmetry and a new exotic particle becomes relevant at high temperatures.